I am a CS major guy and don't know a whole lot about EE so my opinion will be biased. In my opinion CS has a better future because the talent in this decipline is hard to come by. We are struglling to fill positions as we can't find people with CS degrees. Most of the Americans want to graduate with easier degrees (Social science, Art etc) hence it leaves a gap in the CS area. This probably applies to EE as well. For next 15\20 years CS majors will not have problem finding a good job.
Another aspect of CS is that once you know few programming languages you can go anywhere in the world and find a job, not sure that is valid for EE.

Icanfly