They are remarkably similar, but, there are differences. The P3, for instance, can handle both electric and hydraulic brakes...if you need both now (multiple trailers) or may in the future buy an upscale trailer with hydraulic disc brakes then the P3 would be the way to go.
What sold me on my P3 is that all the controls are on the front face plate. In my Jeep, I've got the brake controller (P3) mounted darn near vertical against the knee rail to the left, near the door. There isn't enough space to reach any controls on the top. The P3's display is also "flat" to the front mounting plane. In the P2, there are controls mounted to the top and the display is angled. If the P2 is going to be mounted "topside", i.e., on top of the dash, for instance, it would work equally well as I think the "guts" are the same. In my mounting area, the P3 had the layout that works best and was worth the extra $50 in cost. It is low, out of the way, yet I can operate all the controls and with the display flat to the front, a glance down tells me all I need to know.
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)