I've not yet finished a game, but played through various bits of four separate ones.

the new (?) mega event that spawns pirates all over the galaxy happened in all four, and seems to have taken the place instead of the Plague event in terms of, the frequency of the event. It happened in all four games, and it's a serious blow to the galaxy. Even the AI takes a serious dip in military ability as their ships are blown to pieces, and their Starbases destroyed one by one. Though, in the 4th game I did manage to finally return fire and get out of the strangle hold they had on me and my planets, and eventually the AI coped with most of them as well.

I noticed the Strength of the pirate ships scales in relation to when it happens, late game has more powerful pirates then earlier, so it seems to be based on some average tech lvl throughout the galaxy. It's a fairly potent event though, and perhaps a tiny itty bit too harsh, or maybe I need to micromanage better and stop sucking.

Another trend I've noticed, and I saw this in 1A too, but rarely if ever in the orig. game, is the AI having multiple Allies. Take the latest game I was playing, one of the biggest powers in the galaxy was the Arcean for the longest time, then the pirates came and a bunch of other more minor events happened, and eventually the Thalans were between #1 and #2, with the Iconian Refuge, whom I'd traded with since the beginning of trade tech availability, and generally tried to keep on my good side showing up as #1 in military power, viewed as the most powerful of all the races.
So, without looking at the current relations of the Thalans, (I know I should have), I thought it be wise to attack them before they get even more powerful and so I setup a force to take the four planets of theirs they had near my home worlds. Upon attacking them though, several of the other races came to their "rescue".

In fact, they were allied to all but the Korx and my self. That gave them the Iconian, Drengin, Arcean, Terran, and Krynn as allies all stepping up to the plate when I attacked.
Hello Galaxy in other words.

This I found a bit frustrating, as the AI generally hadn't been very forthcoming in wanting to trade Economic/Research treaties (it hadn't at all in fact), or techs. Most of the times it was moaning at me that one of the other races were attacking them or growing too large for their own good.

I suppose I should have been more aggressive in winning over more races, and maybe allying one or two. But it'd be nice if the AI were, at times, the one approaching me with Alliances. I've noticed it doesn't research the Alliance tech that often either.

That said, some other things that I thought was worth mentioning.

The spy system is better, but I'm not a fan of ultimates. It still requires X agents on a planet to increase Espionage level, rather then it being something that happens over time as with the orig. game.
I still long for a more elaborate system, based on percent chances of success, in blowing up planet improvements, assassinating planet officials to possibly delay production for X turns, or steal techs from other races. All with chances of finding out who sent the agents.
The counter espionage option is also bottom line nice, but again it's an ultimate rather then a %. Spy invulnerability is a bit too much. I'd rather see the planet improvement you build lend a % chance towards capturing spies on the planet it's built on, or help train Agents. Or Separate structures that functions as either a training facility or a anti-agent police force.

I've noticed that morale i a fair bit harder to keep up then in 1A or previous games, overall it seems to be for the better. Have to actually build the approval improvements now.

Some pet peeves of mine, or one of them, is the Galaxy size. It'd be nice if there were a custom option to set a size of your own choosing, or an option between Large and Huge galaxies.

Another is Starbases, still too much micromanagement and constructor building for me to bother with mid-late game, having to build up 12-15 modules is just, urgh. Some type of auto-update or auto-build over time mechanism is something I long for.

I find that I miss some type of Planet Defense system that isn't ships. Some kind of planetary Missile/Beam/Mass Driver battery, or orbital space station ala the ones in Master of Orion.

Anyway this is getting long winded so I'll round it off, obviously it's also down to personal preferences, but thought I'd mention it anyway. There's possible things I've forgotten, but that'll have to be for another thread/post.