I'm speaking strictly about the paper wallets that print out the raw private key, and
not about wallets that ask users to backup their mnemonic seed.
This type of wallets has a lot of flaws:
You need to use printer to create it, which can be malicious. Especially f it's owned by a third party like a store.
They create just one address, which means you'll be tempted to reuse it to receive multiple transactions.
According to
Bitcoin wiki, they have less error correction than seed phrases:
QR codes were not designed for secure storage of cryptographic material. QR codes have been damaged and made unscannable by water, crumpling and even folding the paper.
As seed phrases uses natural language words, they have far more error correction. Words written in bad handwriting can often still be read.
They are often generated by websites, which can easily be malicious. Example -
https://bitcointalksearch.org/topic/vulnerability-discovered-on-bitcoinpaperwalletcom-do-not-use-it-5249129A mnemonic seed wallet has many advantages - you only need pen and paper to make it, it creates a full wallet with as many addresses as you need, as well as change addresses, and you can even memorize the seed to additionally store it in your head.