In both stories, you have some kind of magical spirits/deities/goddesses hanging around the main protagonist.
Both stories give off harem like vibes or cliches with the thought that there will be a love triangle.
When in the end it ends up showing up as solely being a romance series with humorous supernatural shenanigans.
Mamotte Shugogetten! does not follow as clear on its story I guess unless you plan to read the 11 volume manga series instead of watching the anime adaptation.
Ah! My Goddess! is better in comparison to Mamotte Shugogetten!. So take Mamotte Shugogetten! as the bargain bin version of Ah! My Goddess! Mamotte Shugogetten! is a series that is underrated or obscure for good reasons.
I will say that despite the great dislike people have for the Mamotte Shugogetten! anime I still have a fondness towards it because I know it's not the best series out there but it tries to still have fun with itself. Its fondness can be just as strong as one's fondness towards Ah! My Goddess!