Try out bikes of both types and see which ones you like better. The key is fit--sounds like your old bike was too stretched out for you. You may also have ridden with your elbows locked. Whichever bike you get, be sure that the fit is right for you and that you ride with your elbows slightly bent all the time. Strengthening your core through Pilates or planks and the like will help with being able to hold yourself up with our core instead of leaning on your elbows and wrists.

I have bikes of both types. My flat bar bike has bar ends that add a few more hand positions. As the years have gone on, I prefer my drop bar bikes, though.