You can't really compare them, they're totally different.
The Full Moon parties are just pure madness, lots of tourists all together on the beach, different music, different people, lots of fire shows, things going on etc. But they're not a proper clubber's night out because there's not really any known dj's, the people there are just there to party rather than to do some serious clubbing.
I'd say the Full Moon parties are more of a general funny night out, good for a laugh, but you'd never go there expecting to hear serious or well known dj's.
The clubs in Ibiza are proper clubs, all enclosed although you can still find a few beach parties. Everyone who goes to these clubs will be proper clubbers, people generally don't get drunk, there's obviously a lot of drugs going on inside the clubs, you will hear and see some massive world-reknown dj's and hear some amazing sets. You do get some tourist-types who are there on their first ever clubbing holiday who do act a bit ker-azee but generally in all the big clubs you find people who have been going to Ibiza for many years, know all the nights that are on, which dj's are playing, and which tunes are being dropped!
So you can't really compare the two, if you know anything about clubbing then you'll enjoy Ibiza more. Infact, you'll probably enjoy Ibiza more even if you don't know anything about clubbing