I've always found fallen timber to be better than standing timber, as it seems to give the fish more hiding spots, different depth levels to suspend in, more shaded areas, and more ambush potential. Even trees leaning at an angle, with or without tops/branches or totally submerged or not, seem to hold bigger schools than even a group of standing timber trunks. It's a little more equal, though, when there's a root wad or multiple branches in the group of standing trunks.
Kinda works the same way at bridge pillars, sometimes. A pillar that's basically "clean" all the way to the bottom will still hold fish, but when there's some waterlogged debris that has collected on the down current side of the pillar ... there's a better chance of fish holding on it, current or not.