For me, yes because quality-wise, vaccines in health centers are relatively the same as the ones given by private pedias as these are distributed by the government. Although sometimes, the type varies. Say for example, in a private pedia, a Penta + Hib vaccine may be the acellular type meanwhile, in health centers it could be the whole-cell type, or vice versa. This is also why some babies develop fever as a reaction. Acellular vaccines (usually higher priced than whole-cell) does not initiate fever as an effect while the other does. Another factor would be convenience. Sometimes, there are vaccines that aren't available in health centers, like PCV.
Yes, I had my eldest vaccinated in hospital and cost me a lot of money, while my youngest vaccinated in health center and I got the same result, well not to expect that my youngest is chubbier and seldom get sick compared to my eldest who was given expensive vaccines. It's really wise to do it in health center, just manage to go there early in the morning because the lines get really long and alot of people and kids are there which will make your kid prone to viruses. So better go there as early as you can.