There are some avid proponents of the eastern express route here. When you get past the "much less climbing and shorter" points, I think some of their arguments have problems. To be honest, some of the best years of my young life were lived in Damascus, VA -- unofficial halfway point of the Appalachian Trail and also on the Trans America bike route -- so I'm biased in the opposite direction. Of course, at least one of the express advocates has hiked through there, so he's seen much of the scenery he's advocating you skip.
Look at the discussions online for the C&O trail. Most of the cycling recommendations will tell you to ride it in September, in hopes of getting dry weather for better trail conditions.
George Washington thought a canal would be a good idea. Decades after his death, it was abandoned. On the other hand, the last battle of the American revolution was at the start of the Trans Am (Yorktown). 10 miles up the road was the colonial capital of Virginia (Williamsburg) where Patrick Henry made his famous fiery speech, and 10 miles further you come to the first "permanent" English settlement in the New World (Jamestown). If you're interested in American history at all, Cold Harbor was some of the first long term trench warfare as the Confederates held off Union troops trying to advance on the Confederate capital, Richmond, for years -- 20 miles further on.
Why didn't the C&O canal flourish? Railroads, like the line from Mineral to the tunnel over the Blue Ridge near Afton, both on the Trans Am, headed for the western Virginia and West Virginia coal fields. (A few days later you'll pass the competing rail line outside Roanoke.)
Scenery? You can look up at 1,500' ridges on the C&O/GAP, or ride over 3,000' ridges and look down at the "Valley of Virginia" on the Trans Am above Afton and up to 5,000' mountains closer to Damascus. With a May start, you've got a good chance of catching Catawba rhododendron in full bloom (though that depends on the weather in the next couple months). Tobacco fields are pretty much a thing of the past, but you'll still pass coal mines, Kentucky horse farms, and some of the oldest mountains in the Americas, the Ozarks, on the Trans Am.
Most Trans Am riders have no problem completing the ride in 90 days or less. Like John (jamawami), I recommend going to see Glacier. I took the Trans Am to Missoula, which involved riding a large scale W taking a day on each leg to get to Missoula from Yellowstone. Taking U.S. 89 could easily save you a couple days, although (a) you'd miss Adventure Cycling's headquarters and free ice cream, and (b) the upper Bitterroot Valley was quite spectacular, as was the upper Bighole Valley.
