We chose the Cottonwood Lakes trailhead over Whitney Portal mostly because of permit accessibility issues. I didn't research whether or not all of the permits for the Portal had already been reserved, but for much of the summer they are so I really didn't even consider this option. Although it would be a shorter hike to get to Crabtree Basin from Whitney Portal, the length of hike wasn't the only factor in my trailhead decision. There are some compelling non-hiking reasons for wanting to go through Cottonwood and Miter basins.
Cottonwood trailhead to Crabtree Basin is probably between 13-15 miles if you go cross-country through Miter Basin, and closer to 22 miles if you take the trail route down Rock Creek and over Guyot Pass. We made a loop of it, heading in the first way and coming out the second because my dad's boots blew up and we didn't want to risk the patch job on rocky terrain. Crabtree Pass is easy, straightforward walking on the south side (there's a well-defined use trail on most of the route) and a manageable class 2 on the north side as long as you pick the right route down. Not sure I'd want to do it in the early season when it's covered in snow, though. How hard it is ultimately depends on what kind of experience you have hiking over class 2 passes with a full pack.
Feel free to shoot me a PM if you want any more information of the non-hiking variety. And if you click on the link in my signature to my blog, and scroll down to the bottom of the report on this trip there, you might find some pictures of interest.