Grew up with a sister 17 months younger... we had many coordinating/matching outfits and during periods of our lives we were the same size. We, of course fought about clothes, but I'm not too sure any measure would have changed that.
The biggest deal for us was drawers, socks and towels of all things. Sister had slightly smaller feet until we were about 10 and 11, so I hated when Mom would buy the same type of socks in two sizes and then they would be hard to match. So, mom started using thread on the toe line to change that. Hated sharing drawers because one was always complaining the other was to messy... two seperate dressers would have probably been best for that.
Towels were a big deal in the family in general once we started taking showers seperately. The person to go last often complained that the first person had either taken all the towels out of the bathroom, or that they were all wet. One christmas Mom went out and bought a complete towel set for each kid, each a different color. If you got caught with another's towel, you owed them a load of laundry to clean their towels.
Underwear was never a problem between us.... we shared underwear throughout our childhood and have been known on occasion to share as adults. There was NEVER a gross factor on that. And ALL clothes (including underwear) were handed down as long as they were in decent shape.
All that to say that I'm not sure that you can get rid of the arguing... its just the nature of close in age and size (or twin) girls. Mom tried marking tags, always getting me pink or greeen and sister purple or blue, different drawers, different laundry baskets, etc and it helped. But until we learned to work it out ourselves and respect each other's belongings, I'm not sure anything was a cure all.