I've played enough now to know what I like and what I don't here. So a good, bad, ugly routine suffices
It runs very smoothly even with a below spec cpu and looks quite good. The environment is much more interactive and 3D tactics are useful. Items also offer more visual changes. On weapons especially this can be quite informative (blood dripping means life steal, fire means added fire damage, and so on).
I like the emphasis on co-op games and the ability to jump in and help out at will. With friends who are actually playing the game, this is very good. With random people who are doing different things, it is less so (as it just makes everything harder to kill). The banner teleport system from town is especially useful. No shared loot is also useful, as it then presumes a reaction of "what did you get?" from a powerful enemy or a series of quests. Smaller games is nice, though I rarely joined D2 on battlenet and mostly played in network/VPN type games instead, especially once they introduced a single player method of increasing the player count (which didn't make nightmare or normal any harder with well-equipped players, but did buff the experience you received for what were usually cakewalks).
The skill/rune system is decent. In general with any build in D2, it was more or less two or three skills being used constantly anyway. Here you can use up to 6 at any one time and if you really need some specialised killing, you can swap out reasonably fast (depending on the difficulty) to use something powerful rather than randomly available points that were often dumped into a spell in D2 that just offer some (slow) killing ability of some special enemy rarely encountered. Its also fairly customisable to use a lot of offensive/defensive skills (once you dump the game's default line). I suspect this and random item use is necessary for replay ability.
The quest/checkpoint structure is nice. The maps also are a little more predictable (it seems like) for finding your way to the next linear point. This was among the more annoying D2 aspects of having to find waypoints or finish a quest before ending a game. That you can backtrack in a quest through the menu is also nice. Overall this retains D2's routine of jumping in for 15 minutes or so and jumping back out into doing other things in life, or burning an hour or so here or there with observable progress being made.
Fewer Pindle type runs are out there. No Iron Maiden instant deaths also a plus. (Inferno is however pretty instant if you're ill-equipped).
No keys are required for any of the chests and some (good) chests will trigger ambushes.
It's far easier to craft useful weapons or armor than the random rolls from the cube or various item quest rewards in D2, while still retaining the random roll factor. Higher level gems I assume is a compromise for no longer having socketable runes.
The stash is shared across all characters, making it easier to transfer items to other characters. And it is also larger.
The combat mechanics overall seems a lot better and makes things like high armor or dodge chances or blocking more useful to pay attention to than in D2 (where dodge was a Zon skill and only Paladins used enough melee combat with shields to actually be blocking anything consistently and only Pikers, Barbs and Paladins bothered with very high armor. For everyone else, there was running away or teleporting).
Things that aren't so good
It seems like only the first (normal) kill of anything drops rares/uniques/etc. This should be changed so that on nightmare/hell/inferno you still get the credit the first time for a first kill and can get a decent drop. You do get a lot of experience and some gold, but this is not very rewarding and satisfying when you expend a couple minutes trying to kill the Skeleton King or Azmodan and get a couple of random magical items that probably aren't very good.
Legendary (unique) items aren't much better or unique than the random items available. They should offer more unique advantages or be buffed some relative to their rarity and status. Given the auction house item setup being used, I'm guessing this is why these aren't uber-powerful like in D2 (where entire character builds sometimes were based around X item), but they do need some help because they're usually just status symbols that sometimes look cool rather than things you actually use in game. To the extent that this makes rare or magical items more useful, I'm fine with that, but these uniques should at least retain useful status of their own accord.
Boss/champion/elite packs are routinely more difficult than any of the main quest bosses; which mostly are difficult because they take a while to kill and have some unique attacks. The packs however can be extremely painful on higher difficulties and offer a lot of killing combination options for any chance at hardcore.
Fewer chokepoints are available. For instance shutting and opening doors or tanking in a doorway used to be a viable strategy against powerful hordes. There are some skills that make up for this (disintegrate is really fun against a narrow path), but there's less of a tactical feel at times and more of just button mashing.
Mercs are more durable and free to use, but deal much less damage and are locked out of cooperative games.
Stat points are automatically distributed. All of them now offer greater potential benefits for any character (for example, dexterity was almost useless for casters in D2, as was strength beyond what was necessary for a piece of armor or shield), and this is fine. Such that it offers a lot less potential customisation for things like armor or weapon selection versus defensive use of attributes (like a ton of hit points or dodge), it is less so. It is probable that the auto distribute is about where you might end up, but you can't create an imbalance for strategic design purposes with your actual character and have to use items to achieve this effect.
There's often no particular reason to use a wand over a sword as a caster type, or fist/claw weapons as a monk versus axes or maces. Most skills are based off of the weapon damage (with a few exceptions like arrow skills for the demon hunter which require a bow or crossbow), which means you may as well take the better damage sword than a wand or dagger, etc. This is like playing a spreadsheet character rather than the role playing aspect. To be fair, class-specific type weapons do offer particular advantages at times, like extra resources or resource regeneration. But these are only trivial concerns at most points versus being able to deal out an extra set of damage. There are also limitations on what you can or cannot use (eg, monks can't use bows). I suppose I can live with those but they are a little against the cause of being able to customise freely.
I'm not entirely sure what the 10 characters limit is for other than that all characters are stored on their servers rather than being singleplayer modes at home use and they don't have unlimited server space. Given that there's less customisation, 10 seems almost excessive.
I'm not sure what purpose gold serves in the game other than to buy items on the auction house. Repairing items is relatively cheap compared to D2, mercs are free (and don't die as quite as easily when soloing, plus are more customised), most items available for sale are mediocre or below your level when you probably want items which are at or above level, and crafting items or gems is mostly expensive in terms of generating resources for it rather than prices. On the plus side, gold is shared across characters so now new low level characters can quickly equip and the game does not provide ready supplies of more money in the form of selling regular or magical items for 30k a pop such that you are drowning in cash.