You should pick the degree that best fits what you want to do. If you really are dead set both on being a software engineer and working for Google / Apple, then you should go for Computer Science. It’s a way safer choice. Computer engineering is closer to hardware, and there are way fewer hardware-type jobs than there are software. I’m not saying you shouldn’t get a degree in Computer Engineering, I’m saying make damn sure you want to work with hardware before you go that route.
Apple would be a better fit for Computer Engineers, but honestly you’re going to need a lot more than a degree if you want to work there.
Being a web developer, I personally do not want to work at either company. I could probably work for Google if I really wanted to, but I’ve never liked big companies and I particularly don’t like Google’s hiring process so I’ll probably never apply.