I find the weird arbitrary definitions a lot of people place on what a Godzilla movie can and can't be are counterproductive in a lot of ways considering just how many different (and dumb) things Godzilla movies have been over the course of their existence. So I just set a lot of that shit to the side.
I don't think either movie is a bad movie, either. I don't understand how/why you could call them that. They're both well made films. They're not bad at all. Neither of them are anywhere near as successful as they want to be, for reasons that are pretty obvious to anyone whose ducked their head into a Godzilla conversation here more than once or twice in the past 3 years.
I don't give a shit how much money Shin cost. I didn't pay to make it, so it really doesn't matter to me.
2014 is more successful at what it's setting out to do than Shin is. That's why I like it better. It manages to stick to its tone and execute it just a bit more successfully than Shin does. Plus, even for as wooden as the acting is (and my displeasure at Gareth Edwards' "skill" with actors isn't a secret) the actors (who are mostly wasted) are putting in more interesting work (barely) than what's happening in Shin Godzilla, whose tone whiplashes artlessly from serious drama to horror to mild satire to broad comedy and back again almost as often as it switches locations and castmembers. Some people seem to regard this as a positive because they've watched a bunch of Evangelion, I guess. I dunno. I don't really give a fuck about Evangelion either, so whatever Anno handicap people keep grading this film with doesn't apply to me.
And even if you wanna grade it on a pure audio/visual/action level, 2014 has a better looking Godzilla, who does cooler shit, for a longer period of time.
I've said before, but Shin Godzilla plays like a flat episode of Parks & Rec that swaps out Little Sebastian for Demon Godzilla. And that's weird and cool except for when it's eye-rolling and tedious. Edwards' Godzilla is often dramatically inert, but it's also a movie that doesn't really depend on its people to deliver its punch, either.
I prefer 2014 to Shin. Not by much. But its enough.