I will do both though I will not be as fanatical about finding all the waymarks in my area. I do not see any real reason to separate the two but also do not really care that there is a separation.
I agree to a point. I'd do BOTH while on vacation/business trips. Quite frankly a lot of greocaches do not offer much of a hunt and are often not that interesting. The geocaches I remember offer a challenge and/or offer an interesting location. I also like geocaches that introduce me to an area which a virtual/waymark can also do. I would prefer a combined profile/stats page and a combined search page.