Let's start with the practical issues, the main practical difference between a blech and a platta is that the platta is a single uniform temperature over the entire surface while a blech can have hotter and cooler spots. So a platta is more predictable, but a blech gives you more options. Regarding the cost, I don't think the difference is significant, and in any event Shabbos expenses are refunded by Hashem
Regarding the Halacha issues, raw food may certainly not be cooked on Shabbos, whether on a bleach or a platta. Food may be placed on either before Shabbos begins, because the only issue is that we are concerned if one placed raw food on a fire shortly before Shabbos that he may become impatient and stoke the flame on Shabbos. With an electric platta that has only a single, unadjustable heat setting this is not an issue, and a blech is considered an unusual manner of preparing food that would remind one not to adjust the heat. The remaining issue is, as you mentioned, reheating cold, dry precooked foods on Shabbos, where actual cooking does not apply since it is already cooked, and we have already determined that stoking the fire is also not an issue with either a platta or a blech. However there is an additional prohibition of doing an action that appears to be cooking. Since a platta is designed and suitable only for reheating and not for cooking, some Poskim permit placing cold dry precooked foods directly on a platta and consider it more lenient then a blech which is on the stovetop, which is the normal location for cooking. According to the more stringent opinion a platta is identical to a blech, but there is still a solution to place the food you want to reheat on top of an upturned empty pan. This avoids any problem of appearing to cook. It must be emphasized and made completely clear that this only helps if the food is both dry and completely cooked before Shabbos.