7E7,
It would seem to me, from your opening comment, that you are seeking a speedy command. If that is the case, then BA is not the solution.
What does matter is whether you are seeking a career. In that career you may want a choice of flying different types and on different - long/short-haul- routes. In that case an LCA is not the solution. In LCA the last year will be very similar to the first. A speedy command, but then perhaps years of boredom doing the same old same. However, familiarity may bring some contentment, or the early command will give oportunity to seek other adventures.
Financially, from some posts, a good life can be had in LCA's at 75% salary. In a major you probably get the same at 100%, and the fringe B's will always be better, e.g. interline.
What is of consideration, and ask some of your peers about this, is that LCA's may retire you at 60, but perhaps you may need to go longer for financial reasons, whereas most majors release you at 55 with hopefully a decent retirement pot to allow you free choice what to do. (please dont start a thread about BA's new pension plans not being final salary).
It all depends whether you are seeking a life style or an elevation in rank. A long-haul command is no big deal. An F/O has the same thrill just less money for doing it. IMHO the long-haul flying should be done by the under 45's anyway, F/O or captain, then revert to short haul. A major will allow you to bid for long-haul types as an F/O, experience the life style and make your choices when command comes later.
It's not so simple a question after all; it depends on your expectations and ambitions.