Thanks everyone for your replies so far, I really appreciate all the insight. Someone mentioned DHL which is a good idea as an alternative to working from LHR. I'll have a good think about that.
Seems like the majority agree BA is the best career choice. I have a question regarding the lifestyle, particularly for those with partners who work full time or those with young families. My girlfriend makes the point that often our days off do not align but at least I am home each night from work so we still see each other. If I was working LH, she may be working on my few days off between trips, and then I'd be off again so we would rarely see each other. How does this tend to play out in reality?
I'd like to stress that I'm not looking for a move because I don't like SH. I very much enjoy it, I fly about 600hrs a year, 2 sector days, and earn a good salary for a relatively junior FO, living close to my regional base. But I don't get to see any of the world in my current job and our contracts and benefits probably aren't as good as a senior BA pilot. I'm also very keen to get a command and the thought of waiting till I'm well into my 40s for a BA LH command is daunting (not that I would knock anyone who is in this position as it's undoubtedly a great career path - and I appreciate that a SH command would be available much earlier). Equally 35 years of flying to the canaries and back seems daunting, but I would hope I'd have other roles by that stage. This is why I find the decision hard to make, if I was at RYR or Wizz perhaps it would be a lot easier to make the jump. Very much a first world problem which I am fortunate to have.
Still very interested in hearing some more views so thanks again to everyone contributing.