I have a brushed concrete aisle with four sections of FRAMED 12' x 12' matted (six 4' x 6' rubber stall mats) whereever there are cross ties. The framing prevents the stall mats from moving and the 12' x 12' area is large enough for working while grooming and tacking up. I have a very, very long and wide barn aisle which we blow to clean with a leaf blower.
In the wash stall we use the non-slip Mayo Mats also known as Cow mats. They have been AWESOME! They are guaranteed no-slip for something like 20 years! They would have been prohibitively expensive to have used in all 24 of my stalls but if I hadn't had a budget, I would have used them everywhere.
Pictures of my aisle and the framed mats are on my facilities page of my website:
I don't have my own barn, but have boarded and worked at a lot of barns with concrete. The concrete has never been too slipper. I was also at a barn with brick pavers and thought they were beautiful but stuff got caught in the spaces- maybe they weren't set correctly. I've been in two barns with asphalt and while I don't find it as aesthetically pleasing, it did have a bit of springiness to it and wasn't slippery at all. I think in both cases it was a barn that had been dirt floor, and it was cheaper to pave the aisle with asphalt than concrete.
We've been doing barn flooring for many years. We love rubber pavers. Paver bricks, rubber or real, we've always found are best cleaned with a Billy Goat-heavy duty vacuum. Otherwise, you're right, stuff gets in between the bricks and it's tough to get out. Pressure washing works but it's a pita. The rubber pavers are pretty impervious to just about everything and are generally non slip but it takes more than a broom to properly clean them.
I had a dirt aisle with a water line under it, so no concrete for me. I have used rubber mats for years without any concrete framework. Yes they need to be reset occassionally, but as I breed, no baby horse has ever been injured on the mats. I can't say that for the 12 x 12 patch of asphalt in front of the barn - a couple of road rash injuries when bringing in silly babies. I really hate to see that and feel for the babies who can't distingush early on between dirt and asphalt. Summit mats (with the bumps) are better and heavier quality than TSC.