The output is always the same if you supply a private key. I tested it.
Enter the same private key and passphrase into bitaddress and bit2factor. You will get a different result, but they both produce the same unencrypted result.
Ah, OK. I meant that I got the same result on bit2factor when I hit "generate" repeatedly with the same private key and passphrase. Thanks for clarifying, good to know.