I would say both Computer Science and Computer Management & Information Systems (CMIS) are the "best looking" degrees. With that said, I majored in Computer Science, but took some CMIS courses as well and found that the Computer Science curriculum was much more rigorous. The CS degree got into database structures (and best practices), algorithms, Software Engineering, Computer Human Interaction, etc. It taught us the principles of what a good software engineering would need, allowing us to apply them upon graduation.
Does the degree matter or not?
Short answer - it depends.
Longer answer -
If you already have years of experience, then the only thing which might be affected is your salary. If you know how to program and can interview well, you should be able to find a job.
If you lack any solid experience, it would be much harder to break into the field without first spending time in an IT-based position (like technical support, entry level quality assurance tester, etc).
Naturally, there is always the exception to the rule.