The attributes listed in this thread are the experiences of each individual and your experiences may differ with your individual birds.
As requested.
The GOOD
They are adorable, roly-poly little munchkins with spotted undersides!
They have fun but thoughtful personalities. Even though they can be funny little goofballs when they're comfortable, they tend to think before acting and, if startled, will frequently freeze in place and pretend to be invisible rather than darting around wildly. They have a neat, deliberate way of walking - foot over foot - and are fantastic at climbing and clinging and hanging upside down. They fly like the other heavy-bodied New World Birds do, like little winged cannonballs. Beware getting hit in the face by one! 
They tend to be hearty little piggies, and LOVE their fresh veggies, fruits, and mashes!!! They also use their feet to pick up food and other objects, like bigger birds do.
Though it isn't universally true that they're "quiet", as I know people have had linnies with noise issues (such as frequent contact calling.. ouch!) I will say that of my birds (conures, budgies, cockatiels, linnies), they ARE probably the quietest overall, at least in terms of frequency. My boys get going in the afternoon or evening sometimes, with their weird little monkey chatter, and they'll start calling in the morning sometimes if I don't get up early enough, but in general, they tend to be fairly quiet.
They are cute, curious, delightful, and (I think) the perfect size for a small bird!
The BAD
For whatever reason, they tend to become hand-shy after a certain age, even if handfed and raised. It doesn't happen with all of them, but it does seem to be very, very common. I don't have a problem with it, but some people might.
I have found that they are less forgiving, more sensitive, and less adaptable to change than some of the other little birds - again, this seems to happen after maturity. My boys were more adaptable when they were babies. I used to socialize them by taking them to work with me.. they had no problems with this at all, and seemed to enjoy it! Now they are far more sensitive to change, and won't even go to bed if I so much as leave a towel or a box on the floor near their sleep cage. (Instead, they'll fly around the room and chortle angrily until I move the offending object.)
Along with being sensitive to how they're handled, they have long memories and do NOT forgive and forget. The last time I had Dorian and Basil's nails groomed, it took them over a MONTH to let me near them again. And I wasn't even the one that did the grooming... they were just that upset by being restrained.
Since linnies are small and like to burrow under object like blankets, furniture, etc., they also unfortunately can be easy to step on or sit on if you are not careful to be aware of where they are at all times. I know that sounds like common sense, which it is, but a linnie will burrow under your couch, under your pillows, in the cracks between sofa cushions, etc! And they will then sit there as quiet as a rock and almost as invisible.. Since Dorian and Basil are cage free during the day, I am always hypervigilant to look for them as soon as I enter the bird room, so that I know exactly where they are before I walk around or sit down.
Because they are heavy-bodied, if you choose to clip them, you need to be extremely conservative so that they don't get injured. A linnie that is clipped too much will plummet to the ground like a rock. (A wet linnie after a bath will do the same.)
Some people cite their poop as a negative, though it doesn't bother me. Just be aware that they hold their poop overnight like bigger parrots, and will therefore have a big morning bomb that seems completely disproportionate to their size. (And they might aim it at your other birds, if they don't like them.
)
The UGLY
Linnies are known (and my experience holds this up) to go through a "terrible twos" stage around the age of 8 months to 1 year old. Adolescence seems to be rough on them, and they can turn into wretched, biting, temper-tantrum-throwing little demons around this age. When my boys were this age, I endured frequent flying attacks at my face! They might be little, but they CAN bite hard, and when my boys got ahold of me, they wouldn't let go but would hang on and keep chewing on me. Getting them off was rather farcical, since as soon as I got them off one hand, they would bite and hang on to the other. (It's only funny in retrospect!)
They can also be quite cage and resource protective, and pairs have a strong tendency to gang up on other birds and bully them, even seriously injuring them sometimes. My linnies are fiercely protective of their sleep cage and will, even though they're not in the throes of adolescence anymore, attack me if I mess with it in the evening. (These days they mostly make their angry "back off!" noise rather than attacking, because they know I respect their space.) My pair will also actively chase my other birds away from things if they decide they want them. I would never, ever trust them around larger birds, because they are fearless when they are in that mood.
As requested.
The GOOD
They are adorable, roly-poly little munchkins with spotted undersides!

They tend to be hearty little piggies, and LOVE their fresh veggies, fruits, and mashes!!! They also use their feet to pick up food and other objects, like bigger birds do.
Though it isn't universally true that they're "quiet", as I know people have had linnies with noise issues (such as frequent contact calling.. ouch!) I will say that of my birds (conures, budgies, cockatiels, linnies), they ARE probably the quietest overall, at least in terms of frequency. My boys get going in the afternoon or evening sometimes, with their weird little monkey chatter, and they'll start calling in the morning sometimes if I don't get up early enough, but in general, they tend to be fairly quiet.
They are cute, curious, delightful, and (I think) the perfect size for a small bird!
The BAD
For whatever reason, they tend to become hand-shy after a certain age, even if handfed and raised. It doesn't happen with all of them, but it does seem to be very, very common. I don't have a problem with it, but some people might.
I have found that they are less forgiving, more sensitive, and less adaptable to change than some of the other little birds - again, this seems to happen after maturity. My boys were more adaptable when they were babies. I used to socialize them by taking them to work with me.. they had no problems with this at all, and seemed to enjoy it! Now they are far more sensitive to change, and won't even go to bed if I so much as leave a towel or a box on the floor near their sleep cage. (Instead, they'll fly around the room and chortle angrily until I move the offending object.)
Along with being sensitive to how they're handled, they have long memories and do NOT forgive and forget. The last time I had Dorian and Basil's nails groomed, it took them over a MONTH to let me near them again. And I wasn't even the one that did the grooming... they were just that upset by being restrained.
Since linnies are small and like to burrow under object like blankets, furniture, etc., they also unfortunately can be easy to step on or sit on if you are not careful to be aware of where they are at all times. I know that sounds like common sense, which it is, but a linnie will burrow under your couch, under your pillows, in the cracks between sofa cushions, etc! And they will then sit there as quiet as a rock and almost as invisible.. Since Dorian and Basil are cage free during the day, I am always hypervigilant to look for them as soon as I enter the bird room, so that I know exactly where they are before I walk around or sit down.
Because they are heavy-bodied, if you choose to clip them, you need to be extremely conservative so that they don't get injured. A linnie that is clipped too much will plummet to the ground like a rock. (A wet linnie after a bath will do the same.)
Some people cite their poop as a negative, though it doesn't bother me. Just be aware that they hold their poop overnight like bigger parrots, and will therefore have a big morning bomb that seems completely disproportionate to their size. (And they might aim it at your other birds, if they don't like them.
The UGLY
Linnies are known (and my experience holds this up) to go through a "terrible twos" stage around the age of 8 months to 1 year old. Adolescence seems to be rough on them, and they can turn into wretched, biting, temper-tantrum-throwing little demons around this age. When my boys were this age, I endured frequent flying attacks at my face! They might be little, but they CAN bite hard, and when my boys got ahold of me, they wouldn't let go but would hang on and keep chewing on me. Getting them off was rather farcical, since as soon as I got them off one hand, they would bite and hang on to the other. (It's only funny in retrospect!)
They can also be quite cage and resource protective, and pairs have a strong tendency to gang up on other birds and bully them, even seriously injuring them sometimes. My linnies are fiercely protective of their sleep cage and will, even though they're not in the throes of adolescence anymore, attack me if I mess with it in the evening. (These days they mostly make their angry "back off!" noise rather than attacking, because they know I respect their space.) My pair will also actively chase my other birds away from things if they decide they want them. I would never, ever trust them around larger birds, because they are fearless when they are in that mood.