I've done both for quite some time and my experience is different. However I am in Canada so that may be why. Just want to point out what was not the same for me:
For me Chef's Plate is just Hello Fresh with one extra meal for the same price. We have not noticed any major difference in quality or packaging. You probably wont get any cheese or expensive products like that but to be honest HF never gave you much of that anyways. So while they are cutting costs somewhere to make it a slightly cheaper option (per meal, we still pay the same per week) it really isn't something that's been an issue. After doing HF for several years and now about a year on CP we prefer CP because we get more value for our money.