Overall, this version of the game is a massive leap from Beta 2. Though I'm still playing largely with Tarth because I like their feel, I am compelled to try out the other factions as I get comfortable with the new focus of the game.

General Stuff

• Graphically much smoother. Easy to see where you are likely and unlikely to be able to build. Edges softer, animations smoother.
• Quests are back in and have good rewards. Aside from a teeny bit of balance and random bugginess and strange UI text stuff, they are all good.

Champion Stuff

Pros:

• Though the damage output of champions has been reduced until later in the game with good gear, I think their survivability has been improved a great deal with the modifications to armor, the improvement of the HPs, and the ability to pump your dodge.
• Path of the Assassin is fantastic for bow-users. Just fantastic. Impulsive + High Crit = Very useful opposing army tactical damage dealer. Still balanced though, 'cause they can't do it alone.
• There have been more abilities at level up that I've had to stop and think about. Loves me some significant and exclusive choices.
• Lots of new and varied equipment. That's good, even if they have some strange lateral balance (level 5 weapons being in every way inferior to level 3 ones).

Cons: 

• Too often I'm seeing 5 common abilities which leave me non-plussed. I realize that there are tiers of frequency for a reason, but if we are even to bother with them, we really ought to always have a rare, an uncommon, and three commons, or two uncommons and three commons every level.
• Skill to add defense to tactical auto-resolve? Is this really worth choosing over anything else? Should have an all the time ability with an improved benefit for auto-resolve.
• It might make more sense to have champions on overland level up as you recruit them rather than having set champions scattered over the map. For instance, your first two champions that you choose to recruit are ALWAYS level 1 regardless of who they are. Your next two are ALWAYS level 5, etc. They are valuable resources which the game is keyed around, and to start next to your auto-1st level and then find nothing else but high level champions is pretty lame.

City Building Stuff

Pros:

• WAY more building choices in the early game, with piles to be unlocked through research.
• Plenty of things to build without destroying your economy.
• In absence of one-tile cities, I really like the new tightened city building method.
• I would prefer a simple overlay you could turn on, but I like that you can see ground values everywhere you have scouted that you can settle, and that's ok.

Cons:

• Cities still stall out just below level 3 way too easily. Feels strange to me that the location that I choose as the "land of milk and honey" (Game turn 1) to found my empire can in no way support a level 3 city unless I choose the food improvement at level 2, but there are three locations less than 5 turn's march than easily support up to level 4. I'd like to see a better balance here, in general.
• City level up "benefits" suck. Plain and simple. They are always listed "common", which leads me to believe that there is ever anything different. There is not. They often require a massive amount of production to create (50 turns for an almshouse?), despite being something awarded when a city gains size. They do not increasingly specialize a city as it grows making them feel random and slapped on rather than the physical representation of a city's development.
• City queues still sit stagnant for large chunks of the game. This is wasted volatile resources (production). This devalues cities. This makes cities feel unimportant that they can sit totally ignored or tens of turns at a time. I challenge you to find a single instance of another 4x game allowing this for more than a turn or two, let alone tens of turns. I shouldn't ever think "Oh! that's right, I have cities other than the one gear for producing troops, and they haven't dont anything for 30 turns!".

Magic Stuff

This is an entire separate post, and one that I will probably write in a week or so when I've had more time with Beta 3 and schedule calms down. I like that FE intends to include magic as a mechanic in a 4x game, and that is just about the only thing that makes me happy with the magic system.  At current it is bland, unimpressive, unintuitive, predictable, and totally optional to your success or failure in the game. I think that those five traits are the polar opposite of what magic *is*.

Other Stuff

 We are generally getting into pretty good shape. Systems are being refined, factions are being differentiated meaningfully, graphics are improving noticeably by the update, and stability is significantly better. For many things, we are largely down to UI nitpicks.

* Faction Traits scrollbar renders over top of feature names, and should be fixed.