tl;dr Bad knock off of Hearthstone.
I've somehow got this far in life without playing Magic. A new client was released last week on a Hearthstone-like free to play model, so I thought I'd give it a go.
The new player experience is very well designed. I've played other card games, and there's enough Magic in the background of nerdspace that a certain amount goes in by osmosis. But the introduction is gentle enough that even a complete newcomer with any interest at all could pick it up fairly quickly. Magic has enough mechanics that you couldn't possibly take them all in at once; to get around this everything is explained through very short "skill quests" that each explain one particular point of the rules. You have to play through around 5 of these before you can get started on anything else, but after that the skill quests are offered as and when new rules appear in normal gameplay, so you get to see every rule in action immediately after it is explained. You can expect to see several of these playing through the five campaigns, each introducing one of the five colours (or types of card). It's disappointing, if understandable, that the base cards are not enough to recreate any of the tutorial decks.
Compared to Hearthstone, Magic is a thinkier game. Creatures can either attack or defend, but not both in one round, and targets are chosen by the defender, so attack decisions are more complicated. You can also play cards during your opponent's turn, which means you have to consider far more possible responses to any one of your plays. The mana system of Magic is famously swingy and you can run into problem from drawing lands (mana generating cards) and spells (everything else) in the wrong order.
The business model is very similar to that of Hearthstone. You either buy gold or earn it by completing daily quests to, for example, win so many games with such and such a colour combination, or by winning games against other players or the AI. Gold can be used to buy packs, which have 6 cards from some fixed rarity distribution. There's no dusting or crafting, but there is (will be?) trading, and you won't be able to open duplicates beyond the point where they can be used in a deck. You can pay a small amount of gold to make your cards holographic.
My main gripes with the game are with the client. There were times when I thought I was playing Loading Screen Simulator rather than Magic. Part of this was that the server fell down on release. A few days in I can reliably connect, but it was frustrating completing parts of the campaign and then being told that progress would not be saved as connection with server had been lost. Magic cards are very detailed so you would not expect to be able to read everything straight away, but the interface does not make things easier for you. The playing surface is rendered in perspective, so cards are slanted and also get smaller as they get further away, so it is not always obvious even whether two cards are the same. At the same time there are vast empty black and grey expanses, and you feel like they could have been put to better use.
The game plays incredibly slowly, even after disabling all optional animations. (I wonder if they've been watching Goko as well as Blizzard.) The slow animations are compounded by the constant need to watch timers go round to make sure that your opponent isn't about to play an instant or use an ability. (I understand that MTGO is much worse.) The touch screen interface is not great. You can't swipe out to other programs on Windows 8, or check battery or network status. You also have to double tap to register a click, which after seeing this behaviour in several games I think is probably supposed to allow you to simulate hovering, but it's just an annoyance here. And—I swear I am not making this up—there's a splash screen: after loading the game you are presented with a glowing start button that you have to press before the lengthy process of connecting to the server begins.
One of the curious facts about the existing online Magic was the decision to make it the same price as, or even slightly more expensive than, the physical game, and it's interesting to see Wizards testing the free to play model. The obvious competitor here is Hearthstone. Magic might be the deeper game, but it's not as accessible, and combined with the difference in quality of the clients I think Hearthstone will remain more attractive to the majority of new players.