The answer is not that simple. The first question I ask in response is, "what do you want to use it for? Or what are you trying to achieve?"
Both machines are great and will give you results if used properly but they are not equal in all aspects. If you are a runner, or are training for a running event, then the treadmill is a good option. You can train yourself to run at a target speed or adjust your pace depending on your fitness and goals. Treadmills are also a good option for new runners as the running surface is slightly sprung (or flexible) which is easier on untrained joints and muscles. The better the treadmill you use, the more options available to you in terms of running programmes and level of challenge.
However, if you are not a runner, or you are recovering from an injury to you lower limbs then the cross trainer may be a better choice. The main benefit of using a cross trainer is the use of both upper and lower body at the same time - working the handles as well as the foot plates makes your heart work harder to get oxygen to your whole body rather than just your legs. This in turn increases your base fitness faster and with far less impact on your joints.
The cross trainer is an essential tool in the rehab and recovery of some of the athletes that train with us and it is also a better option for anyone that does not enjoy running or gets joint or muscular pain from running, or even walking, on hard surfaces. Contrary to the popular gym myth, oftentimes "no pain equals gain". You can still work hard but you have to work smart as well. A good machine will allow you to increase the resistance or amount of effort you need to exert so that you can keep progressing.
This is a pretty basic comparison of these two great machines but when it comes right down to it, if you are not into running then go cross trainer as you will get better all-round conditioning. If you run or want to run, then go treadmill.
Whatever you choose, remember that either machine will only give you results if you use them. Check in with a fitness professional if you need help to get the best out of your equipment.