How it's closed doesn't affect your score. It might affect on manual review, but closed by consumer is fine.
The bad news is that you are stuck with this account, even if it's closed, and will get the new account ding, etc.
I normally think that Discover is a class act, but I have some real issues with their dumping of applicants over to HSBC, without a clear advisement ahead of time that this might happen. It's easy to say, Uh, OK, yeah, I guess so, when counter-offered the HSBC version, and then regret it.
It reminds me of Ralphie in "The Christmas Story", up at the top of the slide with Santa, when his mind blanks on the Red Ryder BB gun, and he agrees to a football instead. Glad you clambered back up the slide and got what you wanted! Don't shoot your eye out, kid.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit?
FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007