Significance of ARM SysTick Timer vs. Other Timers?
As answered in comments.

The SysTick if present is part of the ARM core, the other timers are from the chip vendor.  SysTick has a more direct event (think interrupt) to the core where the other times come in through interrupts, not that that matters.  And other timers tend to have more features.

You tagged Cortex-M so this is likely a microcontroller which means you might be doing baremetal which means you can do whatever you want, you decide what timers do what.  If you take some already made RTOS or OS for that chip then they have decided what resources they want to consume and why.  Primarily opinion based as far as that goes.

The systick timer is a lot easier and simpler to get going, and isnt always present, some cores dont have it as an option at all and some as an option (for the chip vendor to decide at compile time), so it has that advantage, although there may be some timers in some chips that are equally simple.

Chip vendor timers can sometimes drive I/O pins or have some external involvement where the systick is AFAIK contained within the core.