I just built a project similar to the one you have in mind, and asked a very similar question in the joinery subforum. Anyway, the answer I got was to either make the grooves afterward with a router, or edge joint everything and sand or plane a chamfer/round over on the planks afterward.
I ended up making a rough chamfer with a block plane, and then gluing up the panel. Mostly did it that way because I don't really like to use my router. It's tricky though, because your glue up has to be nice and flat - you can't really plane it down my afterward. Also you have to clean the squeeze out out of the groove thoroughly or so it doesn't show in the finish. I glued up only one joint at a time for that reason.
I think it came out looking good. However it is going to be finished by my brother and his girlfriend, so I don't know yet if I cleaned up the glue well enough not to interfere with the stain they will be using.
I didn't want to just leave gaps because of stiff getting down in between them. If I were to leave a gap, I'd make it a bit like a picnic table - wide gaps that you can get into to clean, with each plank attached to a batten of some sort.