'Keep me apprised' is very formal, and even a little pretentious. 'Keep me informed' is more neutral, and can be used in any situation. More casually, we could say something like 'Let me know (how it goes)'. There are also several idiomatic expressions we could use, such as 'Keep me up to date', 'Keep me up to speed' or 'Keep me in the loop'.

And when using "apprised", a very common mistake amongst native English users is to instead use the word "appraised", which is more common, but has a completely different meaning. I agree with the other comments, that this is quite formal, and probably even falling out of common usage.

You can also say "let me know" It sounds more casual. But between those two, I think "keep me informed" sounds more casual