777 does more long haul. 777 operation is almost entirely medium/long haul with a few local sectors. This adds up to more time off at home because 777 drivers get their hours done more efficiently (as a generalisation). Down side is that most routes are to the Far East and Dunnunder, which means lots of back of the clock, and very little day flying.
330 does more short to medium haul (generally) which means less days off per month, due to more turn around flights etc. (We get payed in block hours i.e chocks to chocks). The plus side for the 330 is that it covers most of the European destinations, which are by and large morning departures with returns around midnight. (much easier on the body)
The bottom line is that you don't have a choice when you arrive any way, but you may have a choice of changing fleets when you upgrade. By that stage you will have a better idea of what suits.
Qualifications to the above statements are that the whole deal will probably change when the A340's arrive, and then again when the A380's arrive, and possibly again if we ever get the longer range 777-300's.
My spin on which is the best fleet is that it depends on your lifestyle choices as per the above. Not too long ago, guys were jumping ship from the 777 fleet when given the opportunity for an upgrade on the A330. This was largely due to a few rogue elements in the 777 training department. This no longer appears to be a problem. There have been plenty of A33 F/O's transferring to the 777 fleet for upgrades over the last 6-12 months, and all doing well. Each fleet has its pros and cons. I think you will be equally happy on either.
Hope that this is of some help.