Download Xcode from developer site vs install from app store
As far as I can tell, they are the same. The size difference might be due to additional files Xcode from the App Store doesn't download by default, that Xcode from the site might have. 

I have Xcode from the App Store; the first time I opened it it asked to download the Mobile Device Framework to proceed.

I suppose this must come bundled with Xcode from the website. It wouldn't surprise me if it were, as this framework seems to be needed before Xcode can start. I suppose Apple distributes its MAS Xcode with users with stable internet connections and single-install in mind, while the website version for users who might want to deploy it to several machines, in which case it would be a drag to have to download any extra-crucial elements that don't come with the installer package. 

Why wouldn't Apple just put everything that is needed on the MAS installer? Probably an issue with permissions; MAS applications aren't supposed to ask for your password to install. These Xcode components, installed later through the app, might touch delicate areas of the system which the MAS installer has no access to.

My suggestion: If you plan on using a download assistant/accelerator and have trouble with your billing for the MAS I suggest you download from the website.  I doubt there is any difference at all regarding the app itself.

PS: If you do, maybe come back and comment if you had to download any additional components or if it was a full installation straight out of the disk image, as to increase the knowledge of the community for any further reference.