The key is matched to your address, therefore it would be logical that the software gives your old key, as that is registered to your address. So entering the passphrase of the new key would result in an error.
However, I've got two keys (to two different addresses handled by the same account) and when I sign a message, I get the question what key I want to use. So that might be a possibility for you.
Apart from that, it's not the most sensible to do, creating different keys for the same address. The key to this is trust and using different keys for the same address doesn't inspire trust. The best thing to do would be to sign the new key with your old key (so that the trust inspired by your old key gets transferred to your new key) and then revoke the old key and delete it from your keyring. (Maybe after mailing some important contacts about this change of keys, as it would be problemetic when someone woud send you a message encrypted with your old key.)
When you've got a lot of stuff encrypted to your old key, you might reconsider the whole operation.
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I'm just a user of The Bat! I don't work for Ritlabs.