Dropbars deliver a greater potential for comfort. If the bikes are setup similarly, riding the hoods on a dropbar should feel more or less the same as a flatbar. The most significant difference is that dropbars allow alternate handholds that not only change the orientation of your hands, but also change your posture - posture change spells relief. Here's a little experiment you can do:

Sit on your mtb and get someone to take a picture of your profile. Do this for all your possible handholds. Then take pictures of all the potential handholds with the dropbar/aerobar. Note the variety generated by the dropbars. Start adjusting the fit of your dropbar bike (raising the handlebars will probably be the best place to start) with the aim of getting your hood riding profile close to the comfortable profile you have on your mtb. You'll need to ride some serious distances and do a lot of adjusting to get it right, but in the end, I think you'll find that the dropbars deliver more.

Ultimately, go with what feels right.