Maybe i ought to also say: because the stuff that's on permanent display in the London galleries is so exceptional anyway, the exhibitions you get tend to concentrate less on the 'must get the casual punter through the door with some headline stuff' that you'll perhaps see at exhibitions at major regional galleris like the Walker.
Instead they'll probably illustrate a particular point/artist that the gallery feels is interesting - in other words, the gallery is the draw to get punters into the exhibition, rather than the other way round.
To be honest, it's the permanent displays at the London majors rather than exhibitions that'll have your jaw scraping along the floor
If you only pick one, I'd say go for the V&A. And if you pick more than one, dont get the tube - get the bus between them and sit on the top deck at the front