I recently bought a case for my phone with some other stuff for home. In my case I had two packages in one order and the package by the third party merchant came in faster than the rest of the order (which came from Amazon). I think your experience may greatly vary depending on the merchant.
Somewhat related question, does anyone use Amazon Prime? I am thinking to get it but can't justify the extra expense when you can always wait till you need $25 worth of stuff
I did a free trial of amazon prime, and it was awesome to get fast shipments of small orders (less than $25), but you'd have to do a lot of ordering that requires fast shipping to justify the $75 per year. So if you've never done the free trial go for it!