Just a few words of caution: in either situation make it count, and don't go overboard.
I tried to do the 5/3/1 while cutting thing, but I wasn't mentally prepared to lose any strength so it was pretty much a failure. I then said fuck it and decided to just get stronger because I wasn't about to give up any more pounds on the bar. Things are going pretty well now except for my squat and I don't really regret my decision, but really think about where you're going with this. Being fat sucks. When putting on socks is a chore, you know your situation probably isn't ideal. Make sure you're actually getting strong with the fat, or your efforts are pointless. And just because you don't care about your abs doesn't mean you won't benefit from a tighter diet. You don't have to stuff your face with brownies and eat 5000 calories to make good progress.