The main difference is that Mbed Os is the product of arm and supports many boards with cortex-m architecture. You can read more here. We provided the template for CORE2 to use it with the Mbed OS and you can find it on our GitHub here.
At the moment you can use
stm32loader to flash CORE2 with new firmware. The last method uses RPi connector to flash the board so it requires SBC.
Does it make sense to learn a new thing? It depends what you want to do with it. One advantage of Mbed Os might be the fact that it uses the ST HAL libraries for STM32 targets as ‘close to hardware’ layer so you can reuse a lot of code that is out there for more advance stuff. The mbed is also quite easy to learn and it has good documentation. We’re experimenting with this framework at the moment and with good results.
I hope I explained it a little.