 If you liked
Dungeon ni Deai wo Motomeru no wa Machigatteiru Darou ka
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 ...then you might like
Re:Zero kara Hajimeru Isekai Seikatsu
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Both involve the Fantasy genre where there are magical creatures and such, also both have one striking similarity and that is both main characters want to become stronger for the sake of a girl that they have a crush on.
Another thing is that they are both RPG type of series, so there are some jokes such as status, rank, skill and what not.
The trio of Bell, Hestia, and Aiz have a similar dynamic with the Subaru, Emilia, and Rem. You will notice this once you watch both shows. Although there's a massive difference in tone and plot since Re:zero is more serious and tragic and Danmachi is more of the harem and shounen show.