It seems to be commonly believed that Frankish mail was of significantly high quality when compared to the mail used by Muslim horsemen. Most believe that this was simply because European mail was heavier (i.e. thicker rings/smaller ring diameter). Others say that the iron used in Frankish mail is better quality. I know that the mail used in plated mail suits was light, but this kind of armour was introduced after the crusades. What I would like to know is whether there is any evidence that European mail was heavier than Islamic mail at the time of the crusades.

I'd recomend this: http://www.myArmoury.com/feature_mail.html
It should answer your question.
In short though, I believe that there was no difference in weight, save how much one wore.

standardization is more of an industrial era thing

There are a few Islamic sources claiming that they prefer Frankish mail over local mail. Usamah is the best known. His own armour was a jazerant with two layers of mail - one Frankish and one of local make. His comments throughout his book imply that Frankish mail was better able to resist weapons - though the reason for this is unclear.