I would go with blu ray player from a reputed locally available brand that can also playback files through USB (from external hard disk). Prices are more or less similar to Media players, and you also get advantage of being able to play Blu Ray discs. Plus after sales support is generally better as the general BDP brands (Samsung, LG, Sony, Philips) are mostly established with good service presence.
On the other hand, Media players may be more energy efficient, have more user community hacks and downloadable firmware updates for the more established names, and play additional file formats though USB. All the best for your purchase.