For one, some people are more inclined to do one thing versus the other. Many experimentalists, by nature, like to tinker with stuff and are more inclined to build things. Most theorists do not have that inclination. But this is really a very poor generalization.
The best theorists are those who do dabble in experiments and do tinker with stuff. Read Bob Laughlin's description of his childhood. Naturally, when he did become a theorist, his main attention are on experimental results, and he has the knack to figure out which experiments are more "robust" and "trustworthy" than others. If you are a theorist and you have no clue on which experiments to trust, then you might put your eggs in the wrong basket.
Correspondingly, the best experimentalists are those who also have a good grasp of the theory. This is especially true in high energy physics where you not only have to be able to come up with some of the most complex experiments and be able to reasonably predict some range of outcomes, but you must also be able to decipher the results (often with the help of theorists). As Rutherford likes to point out, it is why we are not just "stamp-collecting". Our knowledge of theory makes us not stamp collectors.
There is still this dichotomy because, frankly, not everyone can do everything. It takes a lot of effort to fully understand the theory in a particular area, and it takes a lot of effort to be an experimentalist that require a lot of time to build, design, supervise a project. So besides the natural inclination to do one thing versus the other, there is that limitation of effort and time. So we become one or the other. But that certainly doesn't mean that one can't straddle both sides. It has been done now and then. Bardeen, for example, was instrumental in helping the design of the transistor. Yet, he was technically a theorist, as evident by the BCS theory of superconductivity. So he won the Nobel Prize in physics twice, and they're both for the invention of a device and the theory of superconductivity. Is there any wonder why I admire his accomplishment very much?
Zz.