I've done a few miles on an ST1300. Felt like an old friend (ST1100), but with a little more punch. Reportedly better brakes - my ride did not require really testing them out. Those who have done a lot more miles on both suggest the 13 turns in just a bit quicker, but is not quite as stable on the open highway. Tight twisties might be a bit easier on the 13, the longer wheel base of the 11 feels a bit more planted in long, open sweepers.
Both make terrific long-distance mounts. Both play nicely in the curves when you get there. Both handle 2-up quite well. Some prefer the feel and lines of the 1100 better (one friend has 3 ST1100's and has NO intention of "upgrading" - and he has done thousands of miles on both). Some prefer the modestly punchier engine and sharper lines of the ST1300.
Personally, the biggest advantage of the 13 over the 11 is the electrically adjustable windshield. Keep in mind, a 2003 ST1300 with standard brakes is the only model that does NOT included a power shield. It is adjustable, just manually. All other ST1300 models have the motorized shield.
I am no racer, but I have ridden with friends on 1300's when I was on my ST1100 and they weren't pulling me much at all when I was romping the ST.
The ST1100 is clearly an older bike, but even the ST1300 is getting long in the tooth when compared to the competition. A common lament on the other forums I frequent is the lack of a revised model from Honda. Having said that, both machines are still terrific mounts in the sport-touring line-up, with a stellar reputation for reliability and longevity.
I know one gentleman running a late 90's ST1100 with over 200,000 miles on the clock - and he still rides it in the big IBR rally... -)