In some ways it depends on the "level" of the paint, not so much the brand.
My Fiance and I have a bit of experience - at least with our house... and varying paints.
We bought the house about a year ago - and previously the bank had put some crap paint over the entire house inside (probably a really cheap, flat primer - it soaks up anything that touches it.... anything on your hands, if a dog shakes, it makes and leaves marks everywhere).... anyways.. we've gone and painted a lot of the house so far (3 bathrooms, 3 bedrooms, a small office.... most of the trim.... some exterior stuff had to be fixed and new T111 put up/painted).
Home Depot carries Behr.... we paint trim with that brand (because we painted it white, and, well.... there's about a million shades of white) only because that's what we started with.... it takes at least 3 coats to cover the wood veneer with white. It's the 2nd highest level paint they have (can't remember the name) that's an interior eggshell.
Lowes is a different story - they carry Sherwin Williams (HGTV colors), Valspar, and Olympic.
In my last house I used the top 2 in 1 paint/primer Olympic to cover dark brown with a blue/silver (light) color, and 1 coat - yes only one coat... did the trick.
My fiance keeps finding the HGTV colors - which is sort of annoying... because the paint is 'meh' at best, and is about $32 a gallon for the "Ovation" stuff.... Even to cover our s*** wall paint takes 2, sometimes/certain areas 3 coats to cover.
I don't know the longevity of the Olympic.... but I can say that once the paint is down, it seems to hold up REALLY well, especially in the bathrooms. In the past I've painted bathrooms and in the first month or 2 the paint will weep a brownish tint when hot showers are taken. In this house there haven't been any issues like that at all - including a bathroom that is used to wash the GSD's and our 2 1/2 year old son (lots of water gets everywhere, basically).
I do know that I bought some exterior Valspar - and put 2 coats over the T111.... it soaked the paint in (it was un-primered, but the paint was supposed to be paint & primer in one) and left the wood somewhat exposed during the winter. Luckily it didn't do any damage or warping, and we've since gone back over 2 more coats with a different brand, which the T111 couldn't completely soak in like a sponge.