We've done 4-board at our last two properties - it looks great and is pretty safe, but it is a lot of maintenance. Replacing boards, painting.... however when we moved to our current farm we had the choice of whatever fencing we wanted, and we did 4-board again...
I put up vinyl fencing and have loved it. I wish I'd put up 4 board instead of 3, but the longevity is incredible and there is never any painting. Replacing a section is a no-nail slip in. And I don't get vet bills from anything involving fencing accidents. I had one horse go through at a dead out run and there were pieces almost 100' away, but we couldn't even find a scratch on him. At the time I installed (2004) vinyl was cheaper than board and the same as no-climb. Since I have babies every year I wanted as safe as possible and baby feet will go through most no-climb wire mesh.