Surely this is a false dichotomy. I can't recall ever being faced with a meaningful choice between FR and BA. In the rare cases where they serve the same destination (and I don't count Hahn/Frankfurt as such), I'm going to be swayed towards BA simply because it's a pain for me to get to Stansted (if I lived in Norwich, I might have a different opinion).
When I've been faced with a genuine choice between "full service" and "low cost" carriers, I've usually found that the fares differ by no more than 10% (hey, there must be a competitive marketplace in operation here). Even when BA are more expensive (which is by no means always the case), I'm more than prepared to accept the additional cost for the obvious reasons that have already been stated.
On the occasions where the low cost carrier offers the better service (eg direct flights from London to Aarhus or Tampere), I travel with them without a qualm (though I refuse to part with a fiver for a cheese roll).