Feedbin:
https://feedbin.comThere's a small fee, but it's been absolutely worth every penny. The guy's been able to upgrade servers with demand and spend time on improving the interface (particularly for mobile). There are also third-party apps compatible with it, but I haven't found any of them to be as good as the mobile web interface.
It hasn't been perfect (there've been occasional glitches, mostly involving UI slowness), but problems get corrected quickly and the app has continually improved since I signed up, shortly after Reader died. I've been overwhelmingly delighted with it.
As for app vs. service, I've found services useful for keeping everything painlessly synched across devices and computers. It would depend on your feed-reading habits.