Worse performance, particularly in terms of app startup times
Snaps are mounted as separate filesystems, so it can make things look cluttered in your file explorer or when you’re listing stuff with lsblk
Canonical often forces users to use Snaps even when users have explicitly tried to install with apt. e.g. you run sudo apt install firefox and it installs a Snap
It hasn’t gained traction with other distros like Flatpak has, and Canonical’s insistence on backing the “wrong” standard means Linux will continue to be more fragmented than it would be if they also went along with what has become the de facto standard
There are however benefits of snaps. It works for better for terminal programs, and Canonical can even package system stuff like the kernel as a snap - as you can imagine, this might be a very powerful tool when it comes to an immutable version of Ubuntu.