Will the latest version download my iMovies faster than my first generation?

The speed will be dependent on the network.

The new version only streams, it has no usable storage.

The processor is more powerful by far, but networking is limited to 10/100 Mbps on ethernet and n wi-fi as before.

Both ATV1 and ATV2/3 have more than enough network 'speed' to play compatible media near instantly provided the network connection is up to it, and you are using normal bitrates for the ATVs.