We've done both and they have certainly their pros and cons. The thing we loved the most about starting from Trail Camp was we could roll out of our tent and have the switchbacks literally in your backyard, and later in the day when coming down it was glorious to have your tent there waiting to lay down in after you descended.
However, we enjoy Outpost a lot more as the water sources there feel cleaner, you got shade and it doesn't get as windy. Starting from Outpost was a lot more challenging for our old legs, but it was a very easy 4 mile hike to haul the gear up to that point, we acclimated for two days and then went for it.
This year we're still on the fence on the strategy. Trail Camp feels like you're on the moon, it's boring, but oh so darned convenient when it comes to the push to the summit.