I found this article interesting:
http://appalachiantrials.com/three-g...own-of-hiking/
In brief, it talks about a sort of "mini triple crown" (aka "triple gem") where you hike the Long Trail, the Colorado Trail, and the John Muir Trail, thus knocking off three "gems" that are subsets of their respective triple crown trails.
I've hiked all of the JMT and the parts of the CT and the LT that overlap the CDT and AT respectively. I've not hiked the other parts of the CT or LT.
In the context of thru-hiking each of the full trails, however, I certainly agree that the JMT is a 'gem' of the PCT. The CT perhaps a little less so --- Colorado is incredible, but I wouldn't regard the portion of the CT that overlaps the CDT as being particularly fantastic; GNP, the Winds, the San Juans, other places along the CDT are at least as much 'gems' as the CT IMO. The CT does, however, offer a discrete well marked and well known subset trail, and one that is no doubt well worth hiking (!).
I'm writing this here as I'm no sort of expert on the LT, but my recollection from an AT thru-hike was that the part of the LT that overlaps it isn't super special. Nice, but not a big standout. If I were to pick 'gems' of the AT, I'd pick the more usual suspects: Grayson Highlands/Mount Rogers area, Smokies, I'd more readily include the Shenendoah N.P. if you couldn't drive it, certainly the White Mountains, and goodly stretches of Maine.
This "mini triple crown" is nevertheless a clever idea, I don't mean to quibble with it. It's just that, of the three trails, if I were to pick a "~couple hundred mile" subset of the AT as the "best part", it wouldn't likely include much or any of the Long Trail. Maybe instead I'd suggest "the Whites" (122 miles). Longer, and more impressive IMO than the 71 miles through the Smokies, and also somewhat of a discrete part. The hassle/expense of the AMC system puts me off there slightly however. So maybe if one had to pick a "mini triple crown" set of trails the LT actually is a good choice?
This is one of those philosophical discussions that, I think, require sitting around in a group with alcohol involved.