When it comes to noise, elliptical trainers manage to finish first, in almost all situations. Because all treadmills are operated by a motor, they will make more noise than an elliptical, so that’s a second point for the latter.
As your main purpose for which you want to exercise is to lose weight, you will need to take into consideration which machine allows more calories to be burnt. Treadmills copy running, which is an excellent fat-burner, while ellipticals resemble cross-country skiing, which is not so proficient in the field you are after. Setting up your treadmill to top-speed will really burn those fats, so the score is equal again: one more point for treadmills.
Last but not least, a very important factor that comes into play when comparing exercise machines: ergonomics. Although ellipticals tend to keep your body in a more comfortable position due to their arm handles, treadmills have a great advantage in the fact that they let you have control over the position of your body. Provided that both exercise machines respect a set of general health measures, neither of these trainers can really get an edge on the other. Ergonomics ties both exercise machines.
As you can see, both treadmills and elliptical trainers have advantages and disadvantages over their counterparts, but summing up the score they are equal. It really depends on what you want from your exercise machine. If you need to lose weight and work your lower body, choose a treadmill. Otherwise, if you want to work both your lower and your upper body in equal proportions, or if you want a more relaxing training session, you should choose an elliptical trainer.