Very well said dancrbookl! I think they also may have been slightly jealous of each other or the situation. It's like 2 best friends that what to be the best man at the wedding.

I think perhaps, Lupin had a crush on Lily and Sirius felt that maybe Lupin wouldn't do everything he could to save James...

I think Lupin might have been jealous of the realtionshp between James and Sirius and Lupin felt Sirius was a risky choice because he was a liittle off (Sirius did try to kill Snape)...

Maybe will find out in book 7.