There are more differences than similarities between psychiatry and neurology. They both share the fact that they are about the nervous system. In the strictly clinical sense, neurology deals with the nervous system as a tissue. It is concerned with the mechanisms by which damage occurs in the brain, without real interest in where that damage occurs or what functional consequences that damage has. You may think that neurologists are masters of "where's the lesion?" and they are, but they don't really use this information to help their patients. Basically, you can be an excellent neurologist without knowing anything about functional neuroanatomy. As I've said elsewhere, neurology is basically internal medicine for the brain. Psychiatry, on the other hand, is deeply concerned with the mind and how it arises from brain processes. Historically, so little was known about the brain that it was treated largely as a black box as far as mental illnesses such as schizophrenia or drug addiction are concerned. This is why most psychiatrists today, especially the older guard, are pretty clueless about neuroscience. However, the last 20 years have brought an explosion of neuroscience research that is directly relevant to treatment of these diseases.
The other issue relates to what you like to do day-to-day. Are you into doing physical exams and looking at MRIs, or are you more interested in talking to people and understanding how they feel and why? This is an important point, since even though many psychiatrists are certainly interested in brain anatomy and function (some even have PhDs in neuroscience) and many neurologists are interested in behavior and cognition, few psychiatrists really spend a lot of time doing neurological exams and few neurologists really want to hear about their patients' childhoods for more than 2 minutes. There are certainly exceptions, but I'm saying this to illustrate a point about where clinicians tend to derive satisfaction from their work.
Finally, there is this idea that psychiatry is not really medicine while neurology is. Many medical students grapple with as they choose their future specialty. You spend 3 years learning all of this great stuff about physiology, anatomy, biochemistry, physical exams, etc., and then you get to your psychiatry rotation and find that you are really interested in why your psychotic patient thinks that the government is controlling his thoughts with lasers, or how her childhood sexual abuse contributes to her borderline personality disorder. Then you start to think, Why did I go through all of this medical school stuff just to go into a specialty that my parents wouldn't even consider medicine?
My advice would be: Don't avoid psychiatry just because you are concerned about the "doctorliness" of this specialty. Do what you love. Of course, if you really love doing physical exams and are fascinated by mechanisms of stroke, epilepsy, dementias, and headache, then neurology would be a good specialty for you. Definitely don't go into psychiatry if you aren't interested in listening to your patient's "personal" problems, or tend to zone out when the discussion in rounds comes around to where your homeless patients will go after they get discharged from the hospital. Psychiatry is not just about biological disorders of the brain, but also how people with these disorders fit into a social fabric. However, don't go into neurology thinking that it is the only specialty that will allow you to indulge your fascination with the mind/brain. That may have been the case 50 years ago. These days, it's the psychiatrists who are trying to figure out how specific neural systems are involved in complex cognitive functions, while the neurologists are busy trying to figure out the best way to lower your cholesterol or cure your headache or keep the plaques and tangles (wherever they may reside) from spreading. I'm generalizing, of course, but you get the picture.
Anyway, good luck and I wish you luck in making your decision. Also, OldPsychDoc's post in that other thread is very helpful.