I have been to Mexico, and I have been to the DR. Now, Mexico is huge and I haven't seen very much of it, mainly the Northern parts bordering California and that wasn't that exciting. Other parts are much nicer I hear, and I would love to go see them.
However, chosing between the countries is difficult, as it depends on what you want. I found the Dominican Republic a wonderful country to travel in. Big enough where there were lots to see and do and many different kinds of nature, small enough to let you feel you had really seen quite a bit of it in 14 days.
YES - they did have a mosquitoe problem in December, mainly due to an unusual amount of rain in November and December. But insect repellent worked just fine, so we didn't find it much of a bother apart from one evening where both we and the mosquitoes were frantic. Even the local taxi drivers said they had never experienced anything like it. But again - that just goes to show that this is not the usual situation.
The Dominican Republic is delightfully full of gentle but proud people, lively music, stunning nature and towns that make you feel you are a loooooong way from home, but not so strange that you think you might as well have gone to Mars (that's the feeling you can get in China or Vietnam). If you want the touristic paradise version, just stay at one of the all inclusive resorts, relax, have fun, swim in the pool, fry at the beach, eat and drink and dance in the discos. If you want to see the real country, with all its excitement and contrasts - make individual arrangements and travel by bus. You can really have it any which way you want it. My favourite part of the country so far is the Saman? Peninsula.
Enjoy.
Regards, Susanne