I agree that the trails are popular, but the peaks really are not. I have climbed 42 out of 48 ranked peaks in the Eagles Nest Wilderness (plus a few repeats and unranked ones) and only shared a summit once with someone not in my party. The Vail trails can be quite popular though, and I have seen over 100 people on the trail to Booth Falls before, but they were spread out enough to not feel too crowded.
Buffalo Mtn is the most popular and the only one with a class 1 trail to its summit. That can be easily dayhiked from Silverthorne up in Wildernest: http://www.summitcountyexplorer.com/HIKES/Buffalo%20Mountain%20-%20Hiking%20Trail.htm
Some good class 2/2+ peaks would be Grand Traverse Peak from Deluge Lake, Powell from Piney, Solitude from Pitkin, Red from Wildernest and Deming from Meadow Creek. Easier Class 3 like Valhalla from Deluge or West Partner from Booth are good too.
I have lived in the Vail area for 8 years and been climbing in the range just as long. There is a definite increase in trip reports and interest in the peaks in recent years, but so far I haven't noticed it "getting crowed" on the high peaks. Once you leave the trails you are usually not going to see anyone else. Actually with the early starts most peak climbers have, usually you won't see anyone until you are descending the trail back to the car. Of course I could say the same thing of 13ers in about any range.
I think the rugged nature of the peaks in the Gore and the generally vague route information keeps some people away. Buffalo is the only peak with a marked route to its summit, so people who are used to following trails and cairns tend to be a little intimidated by having to route find on class 3 peaks on their own. Also the traverses can get very difficult and complicated with numerous towers so the peaks tend to be "one trick ponies". Even short traverses can get complicated and time consuming (N-O is .3 miles but really caught us by surprise).
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