Complete the requirements for both - don't shut any doors at this stage.
I am not sure I believe that the difference in psychotherapy between clinical psychologists and psychiatrists is that big. Neither train to be psychotherapists, primarily, it is part of what they do. Clinical psychologists usually train in a scientist-practitioner model where they have a good grounding in the key perspectives and approaches in psychology, research methods and statistics, assessment, personality and intelligence testing, possibly some neuropsychological testing, diagnosis, case formulation, and of course psychotherapy - usually cognitive-behavioral therapy and also some other approaches.
Psychiatrists instead go to medical school where we learn to critically disengage and uncritically digest inhumane volumes of information, much of which is entirely useless. We then go on to gain clinical experience in internal medicine, surgery, obstetrics and gynecology, pediatrics, neurology (hopefully) and of course psychiatry. You become a little less empathic, a little more detached, possibly more cynical. Then we do an internship with at least 6 months of medicine and neurology, possibly more. Then you rotate through various bits of psychiatry (inpatient, general hospital, outpatient, addiction, child, forensics, emergency) where we learn diagnosis, formulation, psychopharmacology, management of complex ethical and legal problems, and yes psychotherapy. The most commonly taught psychotherapeutic modality in psychiatry residencies is psychodynamic therapy with many more programs teaching predominantly a psychodynamic approach than in clinical psychology programs. We learnt CBT too, but there is definitely a greater emphasis on dynamic psychiatry and psychotherapy, perhaps because treatment is usually longer term, and there is a lot more to learn, and indeed unlearn (such as the 'medical model' you mention, whatever that is). Unlike clinical psychologists, we don't subscribe to a particular theoretical model, which weakens the field on the one hand, but also makes it much harder to be criticized, since we are 'pluralistic', 'biopsychosocial', use 'multi-level model', are 'integrative', have 'interactional' approaches, and other meaningless phrases.
Whilst it is true most psychiatrists in private practice do not practice psychotherapy, this is partly by choice. There are geographic variations (i.e. NYC, Boston, California etc. all have more psychiatrists practicing psychotherapy, and more patients willing to go for psychotherapy). Then there is competition from other professionals. If the distinguishing feature of a psychiatrist is that he can prescribe, you can be sure, whether he admits it or not, he is going to prescribe because he can, because it's identity, because that's what he does, whether it's indicated or not. American psychiatrists seem more likely to use a combination of meds and therapy than their European counterparts where there is no incentive to prescribe medication of psychotherapy alone will do.
Yes if you become a psychiatrist, you might be a pill dispenser, but it will be through choice, even if it is one you don't remember making. It will also mean you won't be a very good psychiatrist.
see:
http://archpsyc.ama-assn.org/cgi/content/full/65/8/962
and
http://www.nytimes.com/2011/03/06/health/policy/06doctors.html?_r=2&pagewanted=all