There is quite a lot of outdated opinion on marsh and willow tit, as the former hasn't been properly studied in Britain for over 50 years (and that by an amateur ornithologist rather than a scientist), and latter never fully comprehensively. There are more recent studies from other countries, but the British races are likely to be a bit different from others.
i saw a big 2-page spread by Vinicombe in Birdwatch magazine about 18 months ago, in which he repeated some of the old chestnuts. One is that fledgling marsh tits are almost silent, which is a good id feature when compared with noisy willow tits. Complete rubbish. BWP has propogated some of these, which are now being unravelled a bit. Much of it in BWP holds basically true though, but the details are being sorted out.
Behaviourly, there's not much difference between the two species though. They both have similar strategies and behaviour - both store food, both like 'margins' (eg woodland edge, areas around paths/water etc), both are pretty sedentary, both come to gardens and feeders, both are usually seen in pairs or very small numbers, often in tit flocks. The only major behaviour difference is that willow excavate their own nest hole in rotten wood. However, marsh will often clean out and enlarge a nest hole, or take over a willow tit hole, so that can be confusing.
They are both under study at the moment though, and new work is starting to come out.