Are both pages on the same website?
I recently merged two sites and used the Google Webmaster Tools "change of address" and implemented 301 redirects. That was last week - now link: commmand for both domains is showing the same backlinks. I expect the old domain to eventually dissapear though - right now the link: results are basically a clone of the main domain's results.
AFAIK a 301 passes *most* of the existing PageRank so I'd imagine it would also transfer backlinks as for all intents and purposes in this respect, they are the same thing.
Can take a long time for these things to sort themselves out. Remember site: and link: results are just estimations and not live data. I've seen Google take 3-4 months to remove URLs after implementing 301 redirects - some people have reported it taking longer.
When did you make the changes?