I'd say, if you're talking about just waiting for something, "worth the wait" is the better phrase to use. For example: I waited all day for these tickets! But it was worth the wait. When something involves a little more action, and that time and effort will benefit you, I'd say "worth your while." For example: Cleaning the house while your parents are gone will be well worth your while. (Because when they get back, they will reward you.) It would be worth your while to answer every test question. You might accidentally get some right! But HONESTLY, I usually just say, "Was it worth it?" I think this is the most natural/casual way to ask either.

"Was it worth the wait," in my opinion, is more commonly used (speaking from a US American's perspective). But, yes, both are perfectly natural expressions to say. I think that I'd more typically use, "was it worth your while," in circumstances where someone went out of their way to do something. Example: Person 1: I drove 30 minutes to that new restaurant last night. Person 2: And was it worth your while? Person 1: Yeah, it was alright. Hopefully my explanation makes sense in some way!

You can use either. However, was it worth the wait is probably more commonly used. On the other hand was it worth your while is probably a lot more professional. In college in the US you would probably hear the second option more especially from professors.

I use "it's worth the wait" more often but you can use both terms. but I'd say worth the wait would be more natural.