I just did a test with the supported formats on File Roller (the default archive manager, ak. Archive Manager) and this result is based on the selected .pdf and as you can see it's sorted by Size:

As you can see the Compression Format that won it was: .xz

There is no single most efficient format. They use different algorithms and the efficiency depends on the data you want to compress. Some data "suits" some algorithms better than other. There is no easier way to find out which results in the smallest file than trying.

In my experience 7z and rar give good results. Zip tends to be a little bigger. No experience with other formats though. Hope this helps a little.

EDIT

A little addition: There are file formats that are already compressed, like most audio, video or picture files. If you compress those you don't save very much space. In some case (mostly small jpg or mp3 files, but can also happen big video files) the compressed archive can even be bigger than the file.