Sir_fz
Haven't read all replies but just wanted to add my 2 cents. I personally majored in Computer Science mainly because I had extreme passion for programming (scripting at the time) and huge hatred for anything hardware-related. I was lucky to have the opportunity to work with Electronics engineers and personally delve into lower-level programming on MCUs (which is not taught for Computer Science students btw). Needless to say, I find the low-level knowledge of hardware architecture and how the Software interacts with the Hardware is extremely valuable for any good Software and Hardware engineer alike. My point is, I think a Computer Engineering or a Computer Science graduate are both equally capable of pursuing a Software development career, easy (but there's a compromise in the material you're taught which you must seek outside). From personal experience, I found that my Electronics engineering colleagues had very high potential in excelling in software programming more than most Computer Science graduates that I know - for all that matters.
As for which University, can't really argue on that as I think it doesn't really matter. But between LAU and AUB, I'd go for AUB (I've tutored an AUB CS student and I found their program pretty challenging - besides the reputation advantage).