Region-wise you won't encounter any problems, but I don't necessarily see the point in importing one. The only benefits are the built-in storage which is meager anyways and the improved Start and Select buttons which rarely see any use. You could argue that the grip is better, but... myeh - that's hardly a feature. The PSVita 2000 is also slightly lighter, but that doesn't make or break a system.
EDIT: As Tom mentions below, the touchpad is smaller... which doesn't change much either way because you rarely have to use it.
The Phat is perfectly fine as-is and the OLED screen is gorgeous. The LCD one is said to match it in sheer pixel density, but I sincerely doubt that it'll match it in sheer colour saturation and "detail" - I love that OLED, even if it's said to be slightly darker than the LCD screen, since I personally never had any problems with the brightness.
In my opinion, it's really same difference. Neither is region locked, so whichever one you pick will be fine. I personally recommend the PSVita 1000, and if you want to import something, import the 64GB memory card which is great value per gigabyte and hasn't seen a western release yet - PSV-1000+64GB storage sounds dreamy.