Also note that the simple API only includes a single hash for each file, and may use md5 hashes instead of sha256 (technically it may use any of the hash algorithms guaranteed by hashlib, but I've only seen those two). The JSON API will give you *all* the hashes warehouse has for the file, which may be more useful.
Most likely (someone more familiar with Warehouse could answer this) Warehouse will select sha256 whenever it is available, so the simple API may be just as good for you. But it's something to consider.
Best,
Alex Becker