A towel is unsanitary. You'll have to change it before putting dishes on it each time. Otherwise don't bother washing the dishes, putting them on a dirty towel makes them dirty.
A dish drainer allows air to circulate inside the dish, the moisture to drip off and drain, and it allows for the dishes to stand on their side for the moisture to run off. A towel will keep your dishes wet inside and the bacteria will start growing as soon as they sit down on the towel.
Drying wet dishes is also a very unsanitary way to do dishes too. It's actually the most unsanitary thing a person can do. It's strictly prohibited in food service and child care facilities. It's really nasty.
So keep the drainer, it's the cleanest and most sanitary way to allow your dishes to air dry.
If you own your home but don't have a dishwasher perhaps you can start a savings account for taking out a row of drawers or a cabinet section, the plumbing, and buying an inexpensive dish washer. They can be purchased for just a couple hundred dollars at places like Sears.