Depends how much space you have, and how many boards..
I have both systems. Big boards are on flat shelf brackets above the couch, and the smaller ones stand on their tails at an angle to the wall.
I don't think it really matters to the boards unless they have a leaky vent screw, in which case flat, with the screw down is best as it allows any water to drip out again.
Standing up is heaps easier to build, and if the boards get put away wet, the drips are very localised. Boards stored flat on racks drip all over the place..
I also find that the standing up boards are easier to access - but then the big boards are heavier, and sliding them onto a shelf above my head is bound to be a bit awkward!
Have a look at "Sailquicks shed thread":
www.seabreeze.com.au/forums/topic.asp?TOPIC_ID=40828for some inspiration.