Trail runners/ tennis shoes are my preferred shoe of choice unless I'm hiking on rough rocky surfaces or traversing/ climbing snowy slopes etc. Realistically, you're just walking on a dirt path. Comfort and traction should be important factors in your choices. I switched to Altra Lone Peak trail runners a few years ago and have been very happy. Lots of choices of course.
I've only made it as far as Trail Camp before but do not see why a boot would be necessary on any part of the regular Mount Whitney trail.
Some people believe boots can help with ankle support, so if you have ankle issues, you might take that into consideration. They do make very comfortable, lighter weight boots like the Saloma Quests/ Merrils etc, but I don't think any of them are as comfortable or as light as a pair of trail runners.