Is downloading files faster or using steam backup?

I'm confused. You say the two choices are steam backup and download? One implies you already have the game installed elsewhere, and the other doesn't? Either way, what I always do(implying you have the game installed elsewhere) is go to my Steam common folder, copy the whole game folder(Darksiders in this example), and copy it to a USB drive. Then on the new device, I put the Darksiders folder back into the new common folder on the new laptop, then go into Steam, and try to install Darksiders through there. It'll see all the files are there and will say "Discovering Existing files", once it's done finding all the files(much faster than downloading the whole thing), the game will be ready to play.

no need to use Steam Backup (which takes quite some time) - copy game folders to your pendrive, then copy corresponding appmanifest ACF file (it will have game ID at the end) - copy all these thingies to corresponding folders at your new laptop - steam will think DS2 was there installed all time :>

I used this method when I was getting new HDD, and from all the games I had it didn't work for Saint's Row 4 only (had to re-download this one)

just copy and paste the files

i always just backup Steam folder(i mean ALL files,not only common folder with games),then launch Steam.exe after windows reinstall,then press 'Install game'. Steam find existing files,so there is no need to download all(only small dll's etc)