2 rounds lag for the paladin, no cooldown. If you use it while another rally is active it doesn't refresh it and is a waste of a command. With very high morale (edges, etc. in play) it got up to about 14/14 hit and dam and 22 more morale but it was usually more like 8-11 hit/dam. Lasts about 8-10 rounds, its not a 0 hour affect.
Cry of Thunder is "better" in that it comes on a class with on-demand lag and flurry, and turns warcry into a no-lag ability - not to say champion paladins aren't offensive powerhouses, just that cry and marshal are only vaguely similar.
An eagle staff definitely makes the champion look better at sealing kills than usual, which is also true of every other character that ends up with an eagle staff.