Headphones

In a recent video I watched featuring DMS, he said (to simplify) that there are to types of experiences that people go after when choosing headphones. One of them being Maximum accuracy and the other a more lively and fun presentation. I don't think that these are exact solar opposites.

But I do get what he's trying to say, the problem I'm having is that a good big chunk of headphones tend to go the maximum accuracy route.
Am I wrong? For most headphones that I listened to my music (metal, hip hop, electronic) didn't really stood out as much and sounds in a way lifeless. The only headphones that could actually bring some the excitement were the focal clear.

And for this reason I have kind of started to go towards speakers, but still speakers lack intimacy that headphones could bring. Is there a way to achieve an compromise here?