The processing isn't relevant per se, even though it counts for a few anti-paleo points. One thing to bear in mind with the removal of the fat though, is that it might entail the removal of the fat soluble nutrients. According to NutritionData (comparing milks) this isn't so, but this seems a little implausible. One other thing that you lose when you remove the fat, is that the sugar and protein will be absorbed more quickly; even if you don't care about GI, this may practically lead to you feeling hungrier from getting a spike of blood sugar.
Which one is actually better, depends on what you want from the food. The first thing to consider is what two things you're actually comparing. Are the carbs+protein the same in the yoghurts you're comparing (simply +/- fat)? If you're eating the yoghurt for a source of protein then, all else being equal, you might well want to go for the 0% one. I remember when I've been forced to try to meet my protein needs on yoghurt a couple of times (being unable to eat solid food and being unable to cook, respectively), that it was basically impossible to do so using full fat greek yoghurt. By the time I'd reached my daily calories I was still short.
On the other hands, most paleos would say that there's absolutely nothing wrong with saturated dairy fat, but there's (potentially) a lot wrong with casein, lactose and whey, they're also more likely to be trying to increase fat intake than to increase protein intake. In such a case, then the full fat yoghurt is a reasonable food, though it's a shame about the unhealthy sugar and dairy protein. Paleo common sense would probably recommend eating the full fat version just to displace some of the neolithic food, but if you're eating for some specific purpose this doesn't necessarily hold true.
As a general rule the fat free component of the yoghurt would contain most of the micronutrients, (b vitamins, potassium etc), as opposed to the cream, so if you're eating the yoghurt to meet these micronutrient needs then you might want the lower fat yoghurt so that you can eat more of it.