Best smartphone for $200

You could try an HTC m8. That's what I have and I love it. It's a decent size, but it isn't huge. Also maybe the LG G3. Both htc and LG have a newer model out so you could probably find either one pretty cheap. Both are very good phones.

I got the Moto G 2015, coming from the X 2013 like you said. The size jump was bigger than anticipated, but still manageable. It's about the size of a 2014 Moto X (just with bigger bezels/smaller screen), so it's really on the limit of what I can use one handed, but it isn't uncomfortable.

It isn't a flagship device but that's easily overlooked almost everywhere. On the screen, the colors are a little washed out, but that's all I've noticed. Performance may suffer if you're doing hardcore gaming, but for basic use, I haven't noticed any slowness at all, animations and multitasking are super smooth. Camera is much better than I expected, and the battery life is seriously killer. I routinely get a total of 4 hours of screen on time over the course of two days, with power to spare. I haven't tried to kill it in a single day, but I've seen reports of people getting 6 hours SOT.

I can't speak for the other devices you're considering, but I'm confident you won't be disappointed with the G 2015. It really is an upgrade from the X 2013 in every way, except for the display, which is still totally good enough for every day use. I'm very pleased with mine, just be prepared for 2 weeks of shipping, Motorola is having major trouble meeting delivery dates with this phone.