I think a survey of companies that make medical electronics devices would reveal a larger number of EEs than BMEs on the payroll.
The issue for you might come down to what is your primary interest? If you want to help design the product, or the chip(s) at the heart of the product, then you sound like an EE to me. If biology & medicine are more your strength, and you don't see yourself as becoming a circuit designer, than BME is a better choice.
If your goal is to work developing medical devices than the Biomedical Engineering degree is a good choice. It contains electrical engineering courses as well as other engineering courses specific to development of devices for use with the human body.
My dream is to help develop the next generation of medical electronics. Which degree would better qualify me to do this: Electrical or Biomedical Engineering? I am a students at Columbia University in case that's relevent. Thanks in advance for your replies.