Is the BluRay download also 1080p

Both the DVD and the BluRay says they have download copies. But are they the exact same downloads? If I buy the BluRay version, I should get the 1080p HD download version and not an SD version. As I would expect the DVD download version to be SD and not HD.

I had also seen some post somewhere that said on the computer it would be SD but HD if you download onto your iPad or iPhone. That would be awful if as I am currently downloading it on my computer right now to transfer via iTunes to my iPad.

Thanks

Mark