Here are the three things I think they need to do with FATEs (ignoring changes to the combat system and enemy design I feel may also be necessary):
1) Unique rewards for the NMs and hamlet defense recreations. Each major FATE should have its own unique reward(s) or a pool of rewards shared by very few other FATEs. If they don't want to do this with on random drops (likely based on evaluation), then they could have clearing FATEs (again, perhaps based on evaluation) unlocking new purchasable rewards at Grand Companies (or lock current reward behind such barriers in the final release).
2) Doing multiple FATEs within a short a period of time between each other granting a bonus to rewards. Basically, "FATE chains" (or Chains of FATE if you want to get cheesy!). The basic execution of this is that if you participate / evaluate well enough within 30 minutes of your last FATE, you get a bonus. This bonus could increase with more successions. You may need to evaluate higher to keep it going after awhile (I don't see evaluating lower ruining your chain, it just won't count towards continuing it). This would grease the wheels of FATE parties and also have them compete better with leveling dungeons.
3) I mentioned this elsewhere as a more general mechanic in and outside FATEs, but temp-party/auto-party: up to 8 strangers (including parties of strangers if they fit) on an enmity list are automatically put into a special form of party which lasts until 5 to 10 seconds after that enemy has been defeated. All the benefits of a party, none of the hassle. There are more complications (multiple temp-parties for groups of 8+ players, etc), but the point should be clear.
EDIT: If there was one more thing I would, although this starts to get into "battle system" stuff, is have multiple objectives and objectives unique to party roles. If you took hamlet battle and took the stuff DoH and DoL were doing and made it available to everyone, that would be a complex FATE. I would also have to be a harder FATE for it to be worth doing.
Which server is livelier?
Going to say Ultros, but it isn't a really fair comparison as the legacy servers came after and new players were locked for a week longer. Personally I spent more time on Ultros because I didn't want to do the quests to unlock dungeons and such again. I believe Sargatanas has been qualified as a "relatively crowded" server (fully crowded servers do not accept transfers). I believe that means it is quite healthy.