Taken from Wookieepedia
B1 droids often employed sophisticated tactics in battle. Massed parade ranks or simple swarms were used, and they often displayed a concept of cover. During the Clone Wars, however, there was the inevitable development of wartime, and B1 programming began to show some improvement. Nevertheless, their in-battle reactions were often slow, and such initiative as was shown was slight. General Grievous, the commander of the droid army, hated battle droids for their weakness in comparison to the Republic's clone troopers.
I decided to fight for Mandalore, even though I think Greievous has a better probability to win.
I think Greivous would win a few battles, but he despised the B1's, and Mandolarians are better than clones(right?) If B1's weren't good fighting the the clones, they won't stand a chance for Mandos.
After doing some research on B1's they could do many things, and even fight(and some times succeed) in hand-to-hand combat. But Mandos were trained the day they were born in hand-to-hand combat, and I think they would win.