Not knowing exactly, but it seems that for the 3600-series one cant upgrade ROMMON in any other way than replacing the chip. (All but one anyway - 3631 seems to be sw-upgradeable)
You should be able to order
BOOT-3600= Boot ROM Upgrade for Cisco 3600
for free (I think, since it's listprice is 0 dollar) if you have a valid contract
Would be a good idea to check releasenotes for info regarding your card. Or contact the TAC.
Anyway, are you running the same IOS release in both routers?