Umenyiora would never start at DE for the Patriots over Ty Warren.
Warren is 6'5" 300 lbs. Umenyiora is 6'3" 261 lbs... Umenyiora doesn't have even close to what you look for in a 3-4 DE... 3-4 DEs are there to take on blockers and be stout against the run, occasionally making plays behind the line of scrimmage... Umenyiora is a "pin-your-ears-back", all-out pass rusher.
I think the comparison is based on overall talent not the literal sense of switching a Giant's player into the Patriots 3-4 or vice versa.