I went to "top tier" residency and fellowship programs and am going into private practice. The answer is that it depends on region, sub-speciality, practice model, and the job market at the time you come out of training. Cardiology in the big, supposedly desirable cities is very saturated and the vast majority of people coming out of top tier research focused programs go into private practice (along with everyone else), so name / pedigree definitely does matter. If you are willing to move to a mid-sized / small city, or less desirable location it matters much less, but it will still make some difference. However, name recognition is not everything - these top tier research oriented programs do not always provide good hands on training, or training in a multitude of modalities (i.e. they say if you want to do interventional you can't learn nuclear, MRI, pacemakers, etc).... this is key to remember because in private practice you will ultimately be judged / paid on your productivity, and you're not going to be very productive if your only two skils are seeing patients an reading echos!
Hope this helps.