I don't know if there's a difference that you'll notice, but I wouldn't buy a 6.04mm barrel as an upgrade because it isn't enough past 6.05 for it to really be one.
In my opinion.
I always go for 6.01 barrels now, you definitely see a difference in both fps, range and accuracy and I've never had a jam even after using them for over a year. Which is saying a lot when I skirmish just about every weekend.
So long as you don't use your barrel as a shovel and stick to the same brand BBs, you won't have any problems.
from seeing loads of tests,imo the 6.03 is better overall is it lets some air cushion it down the barrel,i used a 6.01 and 6.03 at 2 differrent times,the 6.01 has more range and fps,but isnt as accurate,the 6.03 is a bit less range but like all barrels,to get accuracy you must have a good hop set up aswell