The advanced scanner will save you time - it is a pain in the behind to fly around systems looking for planets sometimes. You can use motion parallax to find most planets without the scanner, but it just saves a lot of time.
Detailed Surface Scanner makes you more money - gives you more information about planets you scan. Worth getting and using, it is kind of fun sometimes to scan all the planets and see which ones are terraformable, which ones aren't, which ones have tons of metal, and interesting to look at the stats on the world and the different atmospheres, different stuff.