If Windows is 64 bit, then either engine should work. I don't know why the 32-bit version would be so much larger - maybe different compiler options? I wouldn't worry about the size as long as it works.
My only concern is that you got these files from the official Houdini web site? (Got to be careful of viruses!)
I have the Houdini engine but I don't know which one to use. I have a fairly old laptop and it's a dual core running on 64-bit windows. Also, the 32-bit version is 6.5mb and the 64-bit one is 2mb, any reason for this?