So far this is what I can gather what is unique about elder scrolls legends:
1. Lanes - minions can only attack other minions in the same lane. Spells can hit either or both. Some minions summon minions in the opposite or both lanes. 1 lane has no special effect while the other gives minions 1 turn of stealth from minion attacks (can be hit by spells or their version of battlecry).
-Just a thought on the stealth mechanic, it does seem to give the "at the start of your turn" cards a lot bigger chance to actually work. Same for lethal (keyword for destroy minion damaged by this) minions.
2. Going second gets you a coin you can use 3 times, but it's not a card. You can't use the elixir (what they call the coin) more than once per turn.
3. Both players start with 5 runes. Runes are destroyed whenever your hero is dropped past damage threshholds, every 5 health. But you can gain health above 30 so you might need to take more than 5 health for your first rune to be destroyed. Some cards are buffed when runes break. But for the player, when your own rune breaks, you draw a card. If it is a prophecy card, you get the choice to play that card for free immediately (regardless of whether it's your turn or not).
-A thought on prophecy cards, they mostly seem like cheap spells or cheap minions from what I have seen. You can fill your deck with prophecy cards in the hope you get these cards out for free when you take damage, but they're poorly stat'd when you have to play them from hand so there is a trade off.
4. Deck size is 50-70 cards. There are 5 colors and you can mix 2. So deck building seems a lot more complex than hearthstone from the outset, as there are bigger deck sizes plus more combinations. There aren't land colors but there are color synergies, such as a minion getting buffed if it's X color, or the next card is X color on your deck.
5. Enchantments. I don't have much to say about this since I've only seen maybe 1 or 2 so far. The one you play in the story increases your minions health by 1. These are permanent (there are minions who can remove enchantments). It was a pretty expensive spell (4 mana).
6. As mentioned earlier, health is not capped at 40. This goes for mana too (I think). Although frankly I haven't been paying attention to whether mana caps at 10 but can then can be pushed past by cards or whether there is just no cap at all. I'll try to look for that. I saw my mana at 11 once after I played a ramp card similar to wild growth.
These are the basic things I can think of off the top of my head. I wouldn't say these are necessarily improvements over hearthstone, but different. And significantly different.
I'm also still playing through the story mode, so don't blame me if I got some stuff wrong. I have played some versus the AI in practice mode though ;