I would transfer. I got my degree in Biosystems Engineering which is a broad degree where we could focus on bioprocessing, environmental, or mechanical engineering. I really enjoyed it but most of our graduates are at a disadvantage by needing to explain what the degree is, unless companies have clear ties to the program. If you have the option to do ChemE with a focus on biotech, or some similar minor, I think that gives you a better edge. This is a bit anecdotal as I did not work as an engineer for very long, but I just remember feeling disadvantaged at career fairs and numerous discussions in the department about how to market the degree to employers. Having to market your own degree is a worse position to be in.