That may depend on what you mean by successful. Without exception the messes I've encountered with the friendliest atmosphere, most popularity among their members and best attended events have been traditional, enforced, single unit, combat arms messes with a traditional attitude (combined with an expectation of fun, hard drinking, and mess games).I suspect there are several impact factors:
1. Mess modernisation - Is it modern? Is it old and tradition filled?
2. Unit - Combat arm / Administrative / Support?
3. Current mess attitude - Old and crusty ******* on PMC or young and vibrant?
4. Nature of mess - Enforced or free roaming?
If you looked at each mess and graded them against those four I'd suggest the winners were modern messes with a decent PMC and an amount of free roaming attendance and events.
Proximity to London seems to make a huge difference as well.
Note that this is only for officers messes. I suspect the same formula doesn't apply to the Sgts mess.