I think that even though many people certified in CCM have had a diverse training experience (ie experience in both MICU and SICU), there are still large differences in competence based on their prior backgrounds. As Kgunner said, the pulm/CC physicians are better suited to managing MICU patients, while the anesth/CC and surg/CC are much better at working in the SICU. We have a combined MSICU at one of our hospitals that's co-run by anesthesia and pulmonary, so I have worked with several anesthesia/CCM physicians. They are outstanding at managing our surgical patients, especially the CT surgery patients, however when we have an anesthesia/CC attending on service, I get very frightened about the management of the medical patients in the ICU. They are great at hemodynamics, airway, and sedation, etc, but I feel that they are very much lacking in knowledge and experience in the underlying problems of the medical patients (such as end stage liver disease, COPD, and cardiomyopathy.). This just points to their original training background -- people who go into anesthesia don't want to deal with medical pathology -- they'd rather spend more time on physiology and recussitation. So they will be much more comfortable when they take care of healthier patients who have a very acute disease (ie surgery or sepsis in an otherwise healthy patient), rather than an acute on chronic process.
That said, most people who do pulm/CC would rather deal primarily with the MICU patients. Again, this goes back to why people choose their original residency. People who choose IM tend to like dealing with complex pathology, multi-organ disease, and various manifestations of chronic disease. You see much more of that in the MICU than in the SICU. As far as the amount of SICU training in pulmonary fellowships, it's highly variable. I just finished interviewing for pulmonary as well, and I've noticed that some programs only have a month of SICU time, while others have a majority of the ICU time in the surgical specialties... it seems like there is an option for everyone based on their preference of mix of patients.
As far as pulm/CC vs IM/CCM, most people trained in IM who want to do critical care will opt to do pulm/CC rather than straight CCM. I think this has to do a lot with marketability. IM/CCM has fewer options as far as scope and arenas of practice. Maybe it's true that it's easier for them to find positions in SICUs as Kgunner has said, but most of the IM/CCM fellows I know are wanting to work in MICUs rather than SICUs. Several of the IM/CCM fellows I know who are finishing up this year have been having a very difficult time finding positions in MICUs, while their pulmonary counterparts have had several offers by now.
To comment on whether you have to like outpatient medicine to do pulmonary/CCM, I really don't think you have to, because you can really tailor the scope of practice of pulmonary to a mix of your choice. I'm going into pulmonary/CC, and I personally really dislike outpatient medicine. (I think I would go crazy if I did more than 1 day of clinic a week.). My current plan is to primarily do ICU and inpatient pulmonary (with a possibility of specializing in interventional pulmonary), and to try to minimize the amount of outpatient clinic time. The beauty of the specialty is that if I decide later on that I might want to do more outpatient time than I thought, it would be easy to change my scope of practice to one that suits my style.