One basic rule of thumb, take everything people tell you with a grain of salt(me too). I can only give advice based on my personal experience, limited as that may be.
1st. Be sure you really want to do cardiology. If you're only a med student there are so many other exciting fields of medicine. I'm not trying to dissuade anyone, but be sure to keep an open mind.
That being said, it is true that the earlier you decide and begin acting on it the better chances you will have on achieving your career goal. This advice applies for any competitive specialty: derm, orthro, ent, ophtho, etc.
You're question: does it really matter? It all depends. I don't know the details, but I'm sure you will get equivalent clinical training at both institutions. I am also fairly positive that you will be in good position for the cardiology match at both institutions.
If all you are trying to achieve is simply match, then it probably does not make any difference. I would poll residents at UTSW and Duke to see how they match. I would imagine that UTSW residents match well, but I would guess they match at good institutions around the region. Duke residents, on the other hand, would match at top tier programs all over the country. I hope I'm wrong, but I bet that is the trend.
If you are a bright young doctor who wishes to become a leader in cardiology, pursue cutting edge research, try out new advanced devices, you'll do fine at both institutions, but I bet more doors open up at Duke than at UTSW.
HOWEVER, UTSW i'm sure has specific strengths that Duke does not have. Almost every major institution can lay claim to having world's expertise in one specific field. You if have a specific interest in that field that UTSW specializes in, then obviously you go to UTSW over Duke.
Again, you will hear the same thing over and over and over again.. If all you are interested is clinical cardiology private practice, then attending any community program is fine. You will graduate with excellent clinical training, and you can have a very very nice practice.
However, all of us want doors to be open. This means access to cutting edge research, first access to advanced devices, heading international committees, setting national policy, taking care of VIP's, consulting for industries, asking to help start up biotech companies, etc, etc, etc. All these opportunities come with a large upper echelon institution.
UTSW vs Duke is splitting hairs a little bit, so do a little bit of research before you jump on the prestige wagon, and most of the comments I made above are really just generalizations that may not apply specifically to Duke or UTSW. The city of Dallas itself may offer more to you than Raleigh-Durham may. Also, you may hate Duke basketball or you may find that you want to go to the west coast or east coast.