Not sure how relevant an LU driver's opinion is here as union membership is spread more evenly across ASLEF/RMT, but here goes.
I think it would be wise when choosing which union to join to consider the quality and qualities of the local reps, as it is they who will be fighting your corner if the time comes. They range from excellent to atrocious, from fair to those who are only interested in feathering their own nest. I have drifted between RMT and ASLEF for this reason (although have never at any point been non-union, nor would I be).
At a higher level I know that I can rely on both of the unions to negotiate well at pay talks so on that front can relax being in either.
Although it might seem logical to go with the majority union (and I guess if I was at a depot where one union had a 99% majority I would go with them), bear in mind that you will get more of a say in local level matters if you go with the one with lesser membership (speaking from experience). Although you should consider too the likelihood of you needing the backing of your workmates, as there is no guarantee that the other union will back strike action in your support.