Well we have been to both a couple of times in the last month. At all BBQ places , I always order with the sauce on the side.
Reflections, BigMistah's brisket is the bomb but so is Bludso's. I like the thicker slices that BigMista does, but that is about it. At both places I order my brisket from the "wet" side. At both places , I had no need to add sauce, the brisket was great.
BBQ sauce: no contest for me. Bludso's is great. BigMista's totally misses for me. Even my son who likes spicier stuff threw it out.
Slabs of Ribs: Perhaps I got BigMista on two bad days (both times in Watts), but his spareribs were not very appetizing both times. Surprisingly they had no smokey crust. Bludso's ribs on the other hand were much tastier and had a very charred appearance, though not as crusty as I like. Actually , I prefer the rib tips at Bludso's (ties for my best with Phillip's). I do not think I will find out if the 3rd time is the charm at BigMista for ribs. Additionally, on the weekends, Bludso's does killer angus beef ribs.
Both serve great Banana Pudding when they have it. (weekends at Bludso's).
The only place in LA that I have gotten brisket that could compare would be Mom's on Imperial Highway (not the Mom's in the valley, which has passable Q too).
For pork ribs, I would still put Phillip's most any day and R&R (on their good days) a notch, and a small one at that, above Bludso's. BigMista's spareribs would not be on any best of LA for me.
Bludso's also has top notch pulled pork and surprisingly decent chicken (which is difficult to do in a pit bbq). I am not a hot link fan, but my son gives a thumbs up to all three types at Bludso's.
I rarely eat sides with my Q. The only side in LA that I would not miss are the beans at J&R.