Typical approaches recommend reading the binary via FileStream and comparing it byte-by-byte.
A checksum comparison will be most likely be slower than a byte-by-byte comparison.
In order to generate a checksum, you'll need to load each byte of the file, and perform processing on it. You'll then have to do this on the second file. The processing will almost definitely be slower than the comparison check.
As for generating a checksum: You can do this easily with the cryptography classes. Here's a short example of generating an MD5 checksum with C#.
However, a checksum may be faster and make more sense if you can pre-compute the checksum of the "test" or "base" case. If you have an existing file, and you're checking to see if a new file is the same as the existing one, pre-computing the checksum on your "existing" file would mean only needing to do the DiskIO one time, on the new file. This would likely be faster than a byte-by-byte comparison.