I can only speak for astronomy here, but I see observationalists/experimentalists and theorists as being equally valuable, but just in different ways. The value of an experimentalist is obvious, as they actually carry out the experiments that further our understanding of science. Theorists, however, have two roles in modern astrophysics. First, they help explain the phenomena we observe in terms of something that we already understand. Second, they help us determine which experiments are worth the time and effort to pursue.
To take some concrete examples, let's say that I go out and observe a star and find its brightness to be oscillating on a period of days and with some measurable amplitude. Although this is somewhat interesting in of itself, the theorist can then go and tell you why it's oscillating (perhaps pressure waves in the star) and then tell you, based on that, what kind of pulsations to expect in other circumstances.
Virtually every major astrophysical experiment that I can think of in recent years has been motivated by theoretical expectations, from WMAP to neutrino detectors. In the former case, the theorists were able to tell us what kind of power spectrum we'd expect from different universes and, thus, allow us to measure various parameters. In the latter, we had very precise models of the interior of the sun that predicted certain levels of neutrino emission from the reactions in the core. This motivated the neutrino detectors and, later, the search for neutrino oscillations.
Now it's true that observationalists will often do some of the theory themselves, so the line can be blurred a bit. I would say that this has become increasingly true with time, so the pure observationalist or pure theorist is slowly becoming a thing of the past. People will usually specialize in one or the other, however, and in the abstract, I don't see any reason that we should be putting more value on one or the other. Theories without observations may as well be philosophy and observations without theories may as well be stamp collecting.
I'm not too familiar with the working of the physics community, but it's hard to imagine that it would be much different.
