Why do some disks read and others won't?

Hey, I have an Xbox 360 Pro 60GB, bought in 2008, that has been struggling to read discs over the last year or so. I assumed it was on the way out, but I've just noticed only certain games don't read immediately.

For example, Oblivion, Fallout New Vegas and Assassins Creed Revelations all immediately go to an 'Open Tray' message after closing the disc tray.

But, Black Ops II will read immediately every single time. All three of those games work on my brothers Xbox, and none are even slightly scratched - what can I do about this?

I've read a lot of suggestions for changing the disc drive but it'd be nice to know what else could be done? Would POT calibration help at all?

Thanks, Will.