Personally, as a professional architectural joiner, I couldn't be without either the bandsaw or the table saw as both are pretty paramount to making an efficient living out of it. If I had to say which one I would keep if I had to get rid of one I would say it would have to be the table saw, or more specifically a Euro-style sliding table saw such as the Felder saws. My reasoning would be that a good table saw is a much more versatile and accurate machine overall as compared to any bandsaw which is primarily a rough working machine, for example, on a euro-style sliding table saw you can quite easily do the bevels, face cuts and trench the cill for a sliding sash window to a very accurate tolerance, you can cut the tenons for doors and sashes with relative ease, and you can use the saw to rebate if you don't have something like a spindle moulder for that. Practices like this, of course, does involve removing the two most important safety devices behind common sense, the crown guard and riving knife. For joinery, it needn't be a 3m sliding table monster for cutting up sheets day-in-day-out, something fairly compact like a Hammer K3, Minimax SC2, or similar would be more than adequate. I would avoid machines without the sliding table purely down to the versatility factor, a saw without one is only really good for ripping though you can make crosscutting jigs to fit them.
Bandsaws have their place and a lot of people prefer them, but beyond cutting curves there isn't much that they can do that a table saw can't do better, but as I said I wouldn't be without both. If you're considering a bandsaw I would say you don't need anything larger than a 14" wheel machine, I find since you typically buy boards in the thickness you want, you never really need to rip material thicker than 4" so all that extra cut height is of little relevance though occasionally being able to cut 9" is useful but very rarely required.
A handheld circular saw is a very handy tool for breaking up larger boards into more manageable sections too, a 9" saw will deal with most stuff you throw at it. Most brands like Makita, Dewalt, Bosch, etc, all make them quite inexpensively and there isn't much to choose between them, they all do the same thing.