Unfortunately there are still some major differences between the 2. XB1 at this point is pretty much a PC it even runs windows 10. The ps4 is a similar story, however it has some cool things about it too. First off, whatever os the ps4 is based on runs off of modified freebsd, meaning it shares a lot of vulnerabilities with it, such that people have loaded Linux onto them through exploits in the web browser. The ps4 also has specific drivers for its graphics chip in such distros as well, and actually runs pcsx2 pretty well. That said there are also some pretty damn cool differences about it, though some are pretty stupid. First off the internal hdd goes from sata to usb into the southbridge, and the only sata device is the bd drive. Next up and arguably coolest, the ps4's southbridge is actually an arm processor connected to the CPU via pcie 4x, and would be what I would want most to become prevalent on PC's (unfortunately this may fall into the management engine crap where you can't see what it's doing and hackers can wreck shop with it)
As for emulators, it's probably always at least worth trying to get it to run, however because the ps3 has a different architecture than a pc, there's always likely to be tremendous overhead. If you don't want to set it up, just buy read dead on ps3 (legally you should also own it before downloading a rom for it), get a long cable/wired controller, and call it a day. It's not worth spending 60$ replacing a Bluetooth adapter when you can probably find the console around the same price.
EDIT: you will probably want to dump all of your games yourself, which requires either a supported bd drive or a cfw ps3, as getting games online is not legal, and is probably a minefield.