I was just curious as to what the requirements would be for transferring from one Science program to another, if anyone has any experience with it. Any idea how it's handled?

Specifically from Queen's Science to Western BioMed or General Science. Does everything transfer correctly?

Thanks

Yes transfer's depend on the program you are transferring to, and the univeristy. Many courses may not always transfer over, and you may have to re-do a year.
This happened to my brother who switched programs from Science to Business, it was very hard for him because they still considered his science courses in his gPA even though he aced his business year, which made it hard for him to later transfer to other universities. Universities tend to hold spots in select programs for their students, and then based on the competetivness of other transfer students, your own grades, and your transfer credits make a decision. It can be a long and hard process... he made it through it, but it takes a lot of effort and you better know what you're getting yourself into
But remember that's just one case, if it's between Universities in similar programs it might be easier, especially if you have the marks to sway them.
Talk to your counselors, and contact their counselors, you can never talk to too many people

I think it is depend on the universities, some universities allow student to transfer their admission one college to another and some of them allowed to change admission from one university to another.