Sometimes anchors are like religion. Everybody has their own beliefs. I was raised in a Danforth house and that's all I knew. About 3 years ago, I tried a 33 pound Bruce with 25' chain and 1/2" 3-strand nylon line. I have been more than happy with this setup. It has held me through two bad squalls, one was a raft up and I had to deploy quick when the other boat's Danforth broke loose. I can manage it up and down without a winch and it hangs well on the roller. It is my primary and I sleep well at anchor even if the wind picks up and shifts. I have effectively changed religions.
That being said, I've never tried a Delta or a CQR. If you are looking for opinions (and we know what those are worth!), I would use my heavy as my primary. Once the wind picks up it's no fun re-setting anchors. For extended cruising, I would have two different types on-board. If for some reason the Delta doesn't bite after several tries, it might be nice to toss down something different. Also check out Practical Sailor which seems to do anchor tests every year or so.
My cruising ground is the Chesapeake and my anchoring is mostly mud.
Good luck.