Ascension is one of two deck-building games that have permanent homes on my tablet. (Star Realms is the other.) I'm not very good at it, but that doesn't stop me from playing a few dozen games every month.
I've only played the electronic version of Ascension, on my Android tablet or PC via Steam. It was a physical game first, but it's a lot easier to play asynchronously online. In person, all the players have to be in the same place and sit down to play the whole game. Online, you can spend a minute or two per turn whenever it's convenient. It may take a week to finish a game, but since you can have a bunch going at once, that's not a big deal.
Part of the appeal of Ascension is the variety available. There are eight sets (and a ninth on the way), all of which can be played stand-alone or in combination with the others. Every set has the same basic building blocks - four factions, hero and construct and monsters card types - but each is distinctive. Several of the sets have extra rules and/or card types, adding extra components to the game. This is another reason playing online is nice - picking out sets and shuffling everything up is instant!
I've played in a few different online leagues, just for the fun of having some structure around playing Ascension games. It's certainly not for the winning, which I do very little of. Regardless, it's still fun to play the same people regularly. I've even done some organizing for the league over at QT3 - it only takes an hour or so each month, and it gives the community there an excuse to play a bunch of games. (And talk trash, in the case of the people who are actually good.)
The Ascension app on my Android tablet isn't the best, sadly. It likes to eat up memory, doesn't resume properly if I turn the tablet off and back on while it's running, and sometimes freezes up. Occasional reboots can help. If I had to name one thing that would make Ascension a better game, it wouldn't have anything to do with the gameplay - I'd rather have a better app implementation.
I keep a half-dozen or so games going pretty much all the time. Sometimes more, in the middle of one league or another. Sounds like a lot, but it's really just a few minutes each day. Ascension is definitely worth a try if you like the deck-building game genre.