I played both.
I will say something in details.
Generally speaking, troops have been rebalanced in a strange way. In my opinion, some units have AP costs that are not correct. One above all: SoK berserkers are TOO expensive, they can be cut down in a moment.
In troop profiles, you got an augmentation of the values of stenght and def. And this is good.
Many new spells have been added to the old ones revised, adding new choices to the list you can play with.
At the beginning of the game, you display unit cards instead of minis, and you place the minis only after. This avoids some "smart tricks" you had sometimes with certain players, who placed the archers and the snipers just in the perfect position to strike down their foes.
Analysing every army, I can say this:
Devouts: They were powerful before, they still are. In second edition you can find a skeleton profile for EVERY other race of the game. As Raga correctly told, this means a LOT of proxies, but maybe it can be worth the effort. Many new spells.
Dwarves: Differently from first edition, they cannot be melted as you like. You have to play with a main clan, covering the 60% of you army total AP cost, and than you can place the others freely. Keepers have got different costs depending on their belonging clan. Many players complain about the fact that dwarves of the second edition are weaker than the first. It is probably true, but in the first edition they were TOO strong. And, in my opinion, some clans have been revised so deeply that they have now a very unique appeal, while they were only support clans before. Of course, you need a lot of proxies here too.
Elves: The elves have been revised wisely, they maintain the houses, you can play only with a certain house, they are incredibly powerful in template effects for magic, house elite troops and heroes are VERY strong, while common troops are little more than cannon fodders. Archers are the best of the game.
Blackblood: They were very strong before, almost unstoppable now. The magician has not the limit of 1/1000 AP, this leads my friend who uses them to place three of them to resurrect the heroes and throwing bombs; goblin units are extremely cheap, and the choice is always wide.
Firstborn: Troops have been generally lowed down in power (especially the iron guard) except for the black sisters, who are the only ones in the game (i think) who still got three actions (many of the units who had this in first edition, such as goblin swordmasters or dwarven axehorn warriors now have got only two in second edition, and I appreciate it). Crossbowmen have been revised in a very interesting way. Heroes are always on top.
Stygians: Heroes have been revised and they are VERY VERY strong. Troops are really nerd. The starved have an increased cost, and the others are good brawlers, but fragile.
Swamp Goblins: They are one of the most re-thought races. In first edition, they were supposed to be played in a high number. Now, they have higher costs, but higher profiles too. Some new units have been added, especially a very nice hero, and they are very interesting to play with, even if I was skeptical about it at the beginning.
Sons of Kronos: They are completely changed. For better! My favourite army. I wasn't able to win against blackbloods before, and still I'm not able to do it now, but in the first edition you had identical profiles for some units, with different abilities. Now, you got very different but skilfull troops to choose, and the troops have got a great compo flexibility, so that you can play mini or maxi warbands depending on the need. The troop who has been revised the most is the slingers. In first edition they were almost unuseful. Now they are incredibly good if played the right way.
Ok, I've said enough.
When me and my friends had to think about the choice to continue playing with the first edition, or use the second, I was really skeptical about the second. Now, after many matches, I can say that I would not come back. I would just change some unit cost (I told my perplexities) and, of course, we ignore the rule that says that if a missile unit (let's say an archer) rolls a 20, ALL THE WARBAND ends it's actions (!?). We just play the old way: HE lost all his remaining actions, the others fire as normal.
I hope this helps.
Have fun.