I always have subs on when it's an option, even when the show's audio is in English. Sometimes I can't catch what people are saying and that bugs me. I'm a fast reader with good peripheral vision, so no issues there (minus the paragraph translations). Plus, Closed Captions can sometimes be hilarious.
For anime, it depends. I almost always have the original language on with subs. I spent 4yrs as a kid watching shows like DBZ and Sailor Moon in Japan and kept practicing, so I know enough Japanese to be able to compare it to the subs and see if they hit the mark. Sometimes TMM wants to have a show on and not have to pay too much attention, so we'll put a sub on. We watched FMA in English, and it's quite good. Haven't watched it in Japanese, got used to the English cast. We've watched the Slayers series in both languages, and aside from Xellos' original VA, they are both great.
There are rare instances where I prefer the dub over the sub. Eg, I caught random eps of Rose of Versailles in Italian around 1999, and Oscar's voice in particular was just fantastic. Italian is close enough to Spanish (which I also speak conversationally) that I could get the gist of it, and I could feel those lines. Sling TV has old anime channels, and I caught some eps in the original Japanese. Decent, but not as great (granted, being a VA wasn't as big a deal back when the show was originally made).
I love all the nuances of Japanese, like having a bunch of ways to just say "I" or "you" alone does not translate. Some stuff def gets lost but some dub VAs can emote the general feeling well. There have been some instances where the Japanese felt flat/overacted, but I can't think of a specific example RN. If I took the same line in Japanese and said it with the same emotional force in English, it would def feel overacted.
On a side note, it baffles me that Crunchyroll's dubs don't include subtitles for written stuff. Eg, on Fire Force and I don't know enough kanji to catch all the words. I think they changed the UI recently, I should see if I can get the Sling app to have dubs and subs on at the same time.