I have a white iP5 and a white LP case. I would think either the black or the white phone would like fine with either case really. I think it just depends on your every day use. I am pretty OCD about my phone. For example, my screen is always clean. I keep a lint free cloth in my pocket at all times along with hand sanitizer. I also work in health care and am not "out in the elements" much or exposed to dirty areas during a normal work day. So, the white is what I prefer and it works for me.
If you are asking if the white is susceptible to dirt like the white rubber parts of an Otterbox Defender case, my answer is absolutely not. The white on the LP case is a hard plastic and doesn't "attract" dirt like the while rubber skin on the Otterbox. I had picked up one of the white rubber/black plastic Otterbox Defender cases, but returned it within 3-4 days because it was such a dirt magnet so I used the grey rubber/white plastic Otterbox Defender until the LP was released. I actually think they may have discontinued the white rubber/black plastic Otterbox Defender due to the dirt issue because it isn't offered on-line and I haven't seen it in any Best Buy or AT&T stores.
My suggestion is to purchase your LP from Best Buy and if you don’t like the white you can return it for the black or vice versa. Also, there is a serial number on the back lower right hand corner of the LP package to be on the look-out for. The higher the number, the better because they are still making improvements to the case. I have returned mine four times, but I'm actually happy with this one.