I am going to be working on an "BeagleBone Black" that will be running an Debian Linux distro.

BeagleBoard.org - latest-images
Current plan is to use "AM3358 Debian 10.3 2020-04-06 1GB SD console"

My questions are about the pros and cons of using an cross GCC toolchain versus an native toolchain.

The programming language will be C.

The pros I know about for cross compiling is that it will normally be faster build times. And, that is the only pro and con I know about.

Tim S.