Which is better in saving space?

I'd leave it installed, it's easier since Steam backup doesn't work very well.

backup

backup compresses the files, installed is fully decompressed.. so for space reasons it'd certainly be backup.. for speedy restoration though raw file backing up is faster.. depends which is more important to you.. speed or space. xD

cleanup savegames can free a lot of space (google where they are for each game). Total War easily uses gigabytes of space with just saves.
I wouldn't use Steam backup, just manually back it up lol.

Steam backup takes forever because of the high amount of data to compress.

If you want to clean saved states of gamea you don't play anymore, try also a nice application, the GameSave Manager. It's purpose is to locate and backup your saves, but you can also use it to locate forgotten files.

It's pointless to install Steam games as backup. Steam versions of games are made to require the client, and Steam has the responsibility to provide the game for you whenever you want to install/play it. When you're not playing a game anymore, you should always backup the saved data and uninstall the game itself to avoid clutter on your disk. (Steam doesn't delete saved data, but for non-cloud games will not help you sync either, so you're better off doing that manually across computers.)

A compression and decompression time... you have to have enough space for both installed/backup versions...

You better delete games and download them again later.