more than just brand, but also consider what series. both brands offer quite a few different 'levels' of component, and these will affect their durability as well (eg: XTR cassette is lighter but at the expense of durability cf XT i believe). as such, it becomes a cost-benefit issue, and what you're prepared to accept.
i personally use shimano chains (incl HG-53/73 and CN-7701) and have had no issues. mind you, i don't ride particularly hard, i'm not a 'clyde', nor have the legs of Jan, and don't usually ride in terrible conditions (mud, rain, sand). so i'm unlikely to break a chain, and don't wear them quickly.
other people seem to swear by SRAM chains ahead of shimano. and i have read various personal reviews with a grain of salt.
as for cassettes, i have a few SRAM ones on the MTBs (and shimano on roadbikes), including the '06 PG-990 (with anodized red spider) and '05 PG-970 i think. no probs so far. other people prefer the XT or XTR cos they're lighter, and XT for overall value and performance.
i personally haven't been swayed either way, and consider the 'better' SRAM and shimano chains/cassettes to be good enough for my needs. one bike came with a SRAM cassette (this same bike has a shimano chain), so i chose a SRAM cassette for the other MTB. and i had no probs with the shimano CN-7701 (dura-ace/XTR) chain on the roadbike, so chose it for the MTB.
yet, cos i don't race and don't ride heaps and heaps nor really hard - so therefore don't put huge stresses on my components - any of this gear is going to be quite adequate. i figure this would apply to others too, but if you are pushing the envelope, then fair enough, take a more measured approach to choosing.
