Well, not really scientific!
Picked up a TRS-XLR cable and used it last night at an open mic. Previously, with this PA system, they had to turn up the gain on my 310ce (using a standard TS guitar cable). Not so last night, had to turn it down at first, adjust the tone a little, and it sounded much richer. There was a guy who had plugged in a 714 (or possibly 814) whose guitar sounded a little weak with the guitar cable provided.
So theoretically, using a TRS cable should not make a difference other than volume, but in reality it really depends on the sound system and the preamp/input section of that PA.