Hi. I hiked the Haute Route in 2008 and the Swiss Alpine Pass Route (Via Alpina) in 2013. I have not done the Tour de Mont Blanc but I believe it is more popular than the Haute Route.
The Haute Route takes you up some pretty high passes and offers alternatives for each segment in the event of poor weather. I left Chamonix August 9 and arrived in Zermatt August 22nd, hiking the last two days via the Europaweg. I had one day of no hiking -the first leg of the Europaweg is difficult. Due to heavy rain, I turned back and waited a day. It was magnificent- best stop was Cabane De Mont Fort, high above Verbier. Also, it runs across the Southern part of Switzerland which enjoys very nice weather most of the time.
The Swiss Alpine Route starts in Sargans, near the border of Liechtenstein and finishes at Montreux. The first few days are very remote for Europe but then gets more typical as you walk west. It crosses the Central Alps in Switzerland with the highlight being in Berner Oberland. Berner Oberland to me is the most magnificent hiking scenery to be found anywhere. It can get touristy in spots but for good reason- it's just grand. It gets more precipitation than the Haute route area but tends toward dry and pleasant weather in September.
The Kev Reynolds books are terrific. They are all you need for any of the routes. You won't be disappointed no matter which walk you choose.
I'm heading to Lauterbrunnen in Berner Oberland next week - this time to just walk my heart out from one place for a couple of weeks. Good luck and Bon journee!