I haven't seen Wishes in person (just via the video here) but have seen Illuminations. Normally, I don't watch the fireworks shows but we were having dinner at Rose and Crown when it started, and frankly, we were completely blown away, it was awesome! I highly recommend it.
Ooops...forgot Fantasmic. Haven't seen it at WDW, only Disneyland, but I still think Illuminations is my favorite.
If you have kids, I think that you definitely need to see Fantasmic. However, if you don't (or if they're older) Illuminations is our family's choice. Last trip, we saw it three times. The music...the synchronization...the fireworks...It's all wonderful.
I haven't seen Wishes yet so I can't comment on that one. But, it's a hard choice between Illuminations and Fantasmic. As much as I love Illuminations, I might have to say I would choose Fantasmic if I could only see one.