LPC1768 vs Timer0, etc
They're different resources for different things.  I can't speak to the LPC1768 specifically, but usually the peripheral timers can be used to trigger or feed other peripherals (i.e., an ADC read or a PWM output) while the core timer can't.  Also, usually the peripherals can be turned off to save power, while the core timer is going to be running anyway.

If it's just going to be there to provide a software tick, then not only is the core timer ideally suited to that, but you can get it working once and then use that code in other Cortex M-whatever devices.