I have been doing a whole lot of different things. Ballet, Jazzballet, Tap , Tae Kwondo Karate (okinawa style) and ballroom (both standard and lating, international)
Today I am still involved with both Karate and Ballroom dancing. Like you describe there are many similarities and things you can cross over. There are also distinctions that can make it difficult to learn specific techniques. I found that once you "understand" better how your body moves using any of these disciplines you really have a head start on many other people in acquiering new techniques.
The perfecting of Kata's in front of karate competitions teaches you the required detail for movements to be correct and easy to execute. This is exactly the same as in trying to learn new steps and techniques in ballroom dancing.
And do not forget the felxibility aspect !
I would not wnt to miss out on both things.
Roland