You can't compare that to each other. A dog that bite is aggressive, a bird that bite is trying to tell you something, bite for protection, or testing the limits. (most hormonal)
When a dog bites you it is always wrong, when a bird bites you it's their normal way to communicate, (just look at them in the wild) and that's why it's not wrong in the same way and therefor you should never react in a bad way when they bite you. Instead ask yourself what you did wrong.
And to get a bite is something that you must expect if you own a parrot. And after just hope that you did learn and avoid that situation next time.
To use a T-stick is one way to avoid that.