It is really hard to say. Let me explain why:

-Traditionally discrete mathematics is tied very well and is one in the same with what you refer to as "computer theory". The very foundations of computing is in pure mathematics... so it would be nonsensical to unlink them.

-The material world tends to work well with real values and error. That being said usually floating point and real valued mathematical problems can be of interest. In particular some realms of real analysis can fall into this picture. This holds for a lot of geometric problems and especially when it comes to probabilities which the medical field needs to use constantly.

Now, with this being said, your secondary question is slightly different than your title question. Pure mathematics should not be segregated from discrete or real mathematics. Its kind of like saying "what is more important to use chemistry or physics", you need one for the other so it doesn't make as much sense to put it that way. If you want to model things on computers, it is discrete mathematics all the way but the results and heuristic based solutions we often see useful in practice require a lot of the time continuous mathematics to properly explain and use them. As for pure mathematics, some of the most important results in "computer theory" are from this domain and are of great importance to knowing what we can and cannot solve in finite time if our assumptions about computers are true.