I can't think Tywin as a military genius. Back in Rhaegar's days he didn't enter in the war but when it was finished, exactly the same as Walder Frey did.
During the battle with the main army of the northern:
a)He was befooled by Robb (a 15 yo boy during his first war) and didn't even imagine that the Young Wolf had split his forces and wasn't with the main army. Even Tyrion wanted to laugh at this failure but couldn't because of the pain of his arm
b)He thought the enemy was far away until he was caught asleep...
c)He placed Tyrion with his savages and sell swords at the left side of his army while the knights and the soldiers at the right. He was sure that the left side will break, the enemy will attack to the brokens and he will encircle them. Well, he was wrong...
d)He won but didn't succeed to catch Bolton, the second most powerful Lord of the North.
Maybe he did other mistakes as well, I don't remember... Seriously, I don't understand why the Lannisters won this battle. Maybe because they had cavalry. All these make me think that if Robb had attacked with whole his forces including his cavalry he would have destroyed poor Tywin's whole power...
Anyway, he then succeeded to win the war because he planed the events with Westerlings, Boltons and the Red Wedding.
In conclusion, he succeeded, finally, to befool Robb but outside of the military events. So he for sure is very cunny but as lord commander doesn't worth a single dragon
Randyll Tarly on the other side led an army that inflicted the only defeat on the rebellious forces of Robert Baratheon at the Battle of Ashford. Who knows if it was an easy victory but with this fact only, we can say that at least he does his job well