so havent played too far yet, but just wanted to give a couple quick things i've noted and wanted to put up a spot to allow others to do the same...
1. Homeworld vs starbases and other core worlds: influence seems to work better now, but you still have to have a really buffed up core planet or starbase right next to whatever you're taking or it's going to take a long, long time. and it gives plenty of time for the civ you're trying to take a planet from to send in as many giant fleets as they have to stop your starbase or core world. The best benefits i've noticed mostly involve the civ's homeworld. this is nice and all, but all the worlds around your homeworld are the one's you're going to want to colonize first anyway to feed your homeworld. so having great influence in the area surrounding your homeworld doesnt end up doing much good unless you're playing on a small, crowded map, at which point i think it would just be op. i think that there should be a little more of a balance between the homeworld influence and the other core worlds and starbases. influence civs should be feared for their ability to reach far beyond their original borders and take you over without offensive combat, not just make it so it's really hard to try to sneak away a planet near their homeworld.
2. time it takes to conquer a world with influence: the most i've seen the planet % revolt move is 6% per turn, even when i had 60x their influence, it still took like 15-20 turns to take a planet. this gives civs plenty of time to send fleets to stop you, and ships blow up starbases and take over planets much quicker than influence does so it gives both sides interesting tactics to work with. influence is def meant to be a slower tactic that requires more time and requires you to be defensive. and paired with defensive abilities it could actually work out very well i think, only thing i think would be more fun for people is to do a better job of pairing influence stuff with defensive stuff, since those both go very well together. (i know that's very vague, but just wanted to throw it in there). the AI still needs to do a better job of actually grouping up and going in to attack together with their ships though.
3. diplomacy with influence: it seems that any time you get a cultural starbase near another civ, it really makes them mad and they end up declaring war on you shortly after, even when i've put a few pts into trying to be diplomatic it seems to lead to war very quickly. maybe the AI should not react quite as much until you've taken over their first planet, giving you time to try to talk things out before declaring an all out war, depending on the civ of course. i think that this would help give players the extra time it takes to get a core world or starbase near other civs and build up and defend them before the other civ really starts to take notice of them. i think influence should be a bit of a sneaky tactic. other civs shouldn't really expect their planets to suddenly turn on them until they've seen it actually happen i think. and tons of stuff already gives you -to diplo with other civs, hard to have +s, esp with all the diff ideologies.