Many will say, myself included that it is easier on a dog to 'lose' a back leg over a front leg based upon balance, weight distribution when getting up/walking etc., co-ordination and that when most dogs do run, it is a three-beat run.
We do a lot of leg amputations at BHRR as we focus on the SN's in our program(s). We have done both front and back leg amputations and all dogs have gone on to lead wonderful and quality filled lives; regardless if it was a front or a back leg.
We even have a tripod, BHRR's Potter; in our BHRR Haven Program at this time having removed his one hind leg due to an aggressive MCT. He was given an 85% chance of having Cancer return within one year post-amputation and he celebrated his one year survival anniversary last November!!!