Firstly, no, it is very likely a coincidence. Both are elite schools and have probably the same weighting application-wise, ceteris paribus.
Secondly, (I'm not a barrister, so maybe some professionals could step up and correct me if I'm wrong) I've attended some pupillage fairs, and many of the chambers I've spoken with say that they do not care about Oxbridge, or they are simply blind to the universities- whether or not that's just to encourage more people to apply, I don't know. I myself, don't see Oxbridge as the be-all or end-all for applications, particularly if you can secure a solid first-class or strong 2:1 degree from a RG uni, plus an array of work experience, debating, mooting, etc (certainly more favourable than a scraped 2:1 from Oxbridge).
That being said, the commercial bar is crazy competitive, and you'll notice a trend when you observe the profiles of many of the junior tenants at the top sets (Essex Court, Blackstone Chambers, 3VP, XXIV, Atkin's Chambers, Fountain Court for example)- they majorly have Oxbridge firsts, and A LOT of other experience (e.g. marshaling in the Supreme Court, work under the Attorney General, legal awards), and maybe a master's (usually BCL).
If you're not at Oxbridge, try as hard as you can to push for a first, open doors for work experience, and ultimately, make your application stand out and look good compared to the Oxbridge grads-as platitudinous as it sounds!