Depends on the genre, but I find a lot to like with both melodic and rhythmically forward music. I love rhythmically intense music with polyrhythms, syncopation, time signature & tempo changes during songs too. I geek out on all that stuff.
I also listen to a lot of mathrock that incorporates all of the above with melodic, often jazz inspired scales, and patterns. It can require the brain for listening. Don Caballero’s album, “American Don”, as a great example of this.
When the rhythm is the melody…
I tend to listen for my brain unless there is a dance floor involved.
I like both rhythm & melody. I see it as a great marinara sauce with rhythm as the tomatoes and melody as the basil, garlic & other spices. You need both, while one without the other can be ok the synergy together is much better. To me some of Joe Pass’ chord melody work with Niels-Henning Orsted Pedersen on bass is a good example of the synergy.
I play music as well as listen to it. I find I can switch between listening with the brain and listening with the body as the needs fit.