Seems to me like GPU failure. If the descrete GPU is dead, the these kinds of symptoms appear. If you try to connect an external monitor or use GPU dependent applications, the system will freeze and/or the screen will go black. You have to force shutdown it.
Here's the way it goes in our household:
I own the 15" Model you describe above (albeit a slightly earlier version with the GTX750M GFX card) and my other half has the 13" you describe above (again, albeit 6 months old at this point)
Now, she does a lot of graphical work on it in Adobe CC - Photoshop, Illustrator, InDesign, etc - much the same as you want to. She says it never skips a beat for her, even when she's running it on external displays in the office and driving the graphics side of things hard. She sometimes gets frustrated with the lack of screen real estate compared to mine (when she does use it) but it's generally not a problem for her. The battery also performs a bit better, which helps if you're on the move a lot. Sure, a bit of extra power would help her but the portability and price trade offs aren't worth it.
Based on what you've said, I'd recommend the 13". It's plenty powerful for what you want, but I would use the left over cash to buy a couple of nice 24" external displays if you have the space to set up a small office. I love having 3 displays running (1 on the MacBook + 2 external.) Better on so many levels!
Another note - it used to be possible to upgrade MacBooks (more RAM, swap out the HDD for an SSD, etc) so I used to recommend buying less and adding to it when you need it. Can't do that anymore, so buy as high spec as you can afford.
Best Answer
This is technically called a 'kernel panic'.
If you want to try a few easy things, follow the instructions on this apple support page regarding this error: https://support.apple.com/en-us/HT200553 Basically install any OS updates available, install software updates for other apps and drivers, reboot in safe mode, reset NVRAM, disconnect all the external devices.
Also you could try a hardware diagnostic by rebooting while you hold down the COMMAND key and the D key at the same time.
However, if you're near an Apple store, I highly recommend making a genius bar appointment to have them take a look at it. They will do a brief look for free, and give you a recommendation for what to do next. Here is the link to do that: https://getsupport.apple.com/