I'll take your comment to mean that you did manage a Half Dome permit. Most excellent. You've likely got this all planned out, but if not I recommend the Mist Trail going up, and the John Muir trail going down. Mist is steeper, and closer to the falls. Muir is longer, but easier on the knees.
For Whitney, I'm guessing that you will have a choice between the chute, and the switchbacks going up from Trail Camp. Not sure which I would take. I've done both, and no doubt the chute is shorter, and steeper, but there is a bit more exposure. For more details see Steve's post at:
http://www.whitneyzone.com/wz/ubbthreads.php/ubb/showflat/Number/55339/gonew/1/Switchbacks_2019 for more information.
Good luck! And enjoy your hikes.
