Depends on the distro. Many distros don't integrate perfectly, some require additional configuration/setup around PackageKit, and there are a lot of customer complaints around various basic issues. One common example: the software centre showing "No Application Data Found". Another common issue: updates don't really work, the workaround is to use the underlying package manager to perform updates.

GNOME's software centre issues very clearly stem from the diversity of package managers and formats and environments it has to support because Linux actually has a decentralized application ecosystem. On Android, F-Droid likes to claim that the "technical skill" needed to install other packages is an artificial barrier which is just imposed by Google, yet it merely piggybacks off the usability & simplicity of Google's centrally developed package formats (.apk or .appbundle) and package manager (PackageManager). When the ecosystem is actually decentralized, GNOME software shows just how user unfriendly things become.