Giving you a private key is better in theory, but it also carries another risk, because you have to trust the service to not use it asap after they give it to you.
It is no more risky than any other method. You still have to trust the mixer with your coins, and a mixer can just as easily claim that you sent coins to a phishing address as they can claim you already claimed the private key.
If you use ChipMixer (do not know other mixer that give you private keys) you get private key after one confirmation after deposit. If it plans to use it (sweep it) after it gives you private key - it may just not give you key at all for same result.
But if you want to maximize your privacy with ChipMixer - you want to add some time between deposit and usage of withdrawn chips. Here is risk that it may steal your keys after day week or month but why would it wait?