I found Shasta in spring much harder than Whitney in summer. The chute does add a whole different challenge -- I did it for my first and only time in May 2013.
In terms of exertion, I found climbing the chute on Whitney (May 2013) somewhat comparable to climbing Avalanche gulch on Shasta (mid-June, 2011 and 2012). I think the chute is shorter distance-wise, but at least as steep if not a little steeper as you gain elevation. The climb to the summit once you get to Trail Crest (Whitney) was easier for me than the climb from the Thumb (Shasta).
Rock falls do not appear to be as much as a problem on the Whitney chute as they can be on Avalanche gulch, but I say this as a nonexpert on such matters. I defer to others on this. The Whitney chute has its own unique challenges (see Kurt W's thread on Whitney Portal store's page about the danger of glissading the chute and its tendency to spit people out onto the rocks).
Will be interesting to see what happens to the 97 switchbacks in the next 2 weeks.
