logged in with same Apple ID but apps haven't transferred

[crmpicco]

I have just restored an iPhone 4 from a backup of an iPhone 3G.

All my contacts, messages, call history and the likes have transferred over successfully. However, my music and most notably my apps haven't been downloaded.

I have logged into the App Store with my Apple ID on the iPhone 4, but the apps aren't downloading automatically.

I am still logged in with the same Apple ID in my 3G - would this cause a problem?

Any ideas why the apps and music haven't transferred over?