I have done the trail several times from Denver to Durango and once from Durango to Denver. IMO, going east to west saves the best for last and is more interesting overall than hiking east out of Durango.
On the reverse hike, the first week out of Durango is a tough one as you climb from 6600’ elevation to 12,300’+, with over 8,000’ of actual climb in the first 30 miles. After that it is daily up down with highs approaching 13,000’ until you leave the San Juans 170 miles into the hike.(about 34,000’ of total climb) Coming from Denver gives you several days of easy hiking and acclimatization before you go high, and even then it is much less extreme.
On the other hand, it is interesting meeting everyone else headed west. When I did it, we did a survey of hikers we met and obtained some really good data which was used by the CTF for planning purposes. (Are you interested in doing that?)
bearcreek