Perhaps not in detail, but in general outline:
* I was able to generate my GnuPG keys myself and I know (to the extent that I trust my computing environment) that I am the only one to have access to the secret key(s),
* the state-approved qualified cert is only a single RSA key, for signatures,
* you don't get to make a backup of that key,
* as a result, it can't really be used for anything else than signing documents, so forget about encrypting data or using it for authentication for example (cases where you really do need to have backups),
* the key is stored on a physically inconvenient device (smartcard) and you need to have one and only one of those,
Plus, of course you get the whole beauty of crappy PKI infrastructure (why does every company dealing with certs have to be shady, have a crappy website and in general be a mess?). But that is beside the point, I guess.