I'm not talking about "social standing." I don't regard either ULaw or BPP as particularly reputable. They are qualification mills. Neither is a university in the ordinary sense. They are busy because they have products to sell which students need to buy in order to become lawyers.
I would choose whichever one is the cheapest (if there is any price difference) and/or most convenient to attend.
To be blunt, those who teach at such places tend to be those who haven't obtained an academic post in a research-led university, and who haven't succeeded at the Bar or as solicitors, so don't go expecting Harvard Law School. This doesn't matter much, because all that the student needs to do is pass the professional exams. People learn how to be a lawyer during QWE or pupillage, as the case may be.
You may see some posts here from ULaw and BPP going on about how fab they are, but that's just marketing. When they say "look at all the people who become solicitors and barristers from here", they omit to mention that this is because there aren't all that many places to do the professional exams.
When assessing pupillage candidates, my chambers doesn't care about where people did the PGDL or the Bar course.
I doubt that many law firms will care much or at all whether an applicant has done the LPC or the SQE, but the solicitors here can comment on that.