In general, it's usually best to minimisse the burden on the most-restricted platform.

On that basis, it makes sense for the embedded system not to use a file system, and to load the burden onto the PC - which has loads of resources to do it!

The downside of this, of course, can be that you need special software on the PC - and the ongoing inconvenience of this to the system users might outweigh the development & target costs of providing a file system.
On the other hand, this "downside" might be an advantage to other systems, where you don't want any Tom, Dick, or Harry to have access to the data!

As ever, there is no simple answer to this - it's a tradeoff based on the specific system requirements. And, as the OP has given no information whatsoever about any of this, it's impossible to even guess what might be "best" for him.