Recording Opinions Please

CD and LP production is a collaborative effort. Of the parties responsible for putting out a recording, who has MOST influence on recording/production quality of the finished product ... the producer or recording engineer? Shouldn't one be able to point to a particular individual and say "... if so-and-so recorded it, I know it's good". Or, are there too many other variables to make such an assessment?
Been in the biz 30 years. In simple terms:

The Producer is the man in charge, hired and paid by the label to craft the sound and deal day to day with the artist in question. Gets profit participation plus fees.

Engineer is more the paid worker bee, usually works in tandem with a producer, and attends to all the technical aspects of the recording sessions and studio environments.

There may be a third set of ears--the person who masters any or all the tracks--there can be different guest producers who have a record of crafting hits (i.e. Timbaland) from the raw tracks using a signature sound. They have a tremendous amount of influence in what you finally hear--many are fix-it people who are brought in when something is felt missing in the mix--six figure to million dollar fees are very common.

The artist also has their Band Manager/ment. The Band Manager is hired to represent the artist interests with the label and the Artist usually has final say over the final mixes and track selections, but can be overruled by the label or producer, who have given the artist the advance, or recording budget. Very few artists have complete creative control (i.e. artist with this include Prince, NIN, Radiohead, Coldplay).

There are many instances where tapes have been rejected by both the producer or label parties.
Easy, the recording engr. that does the final mix. That person is what all the others get to judge.
Thanks for the responses Bongofury (very thorough) and Buconero (concise). I was trying to figure out how to tell - ahead of time - if the CD production quality would be up to par prior to actually listening to certain music. Case in point: I have a lot of jazz that crosses a few labels ... Blue Note, Columbia, Verve, Impulse, Prestige, etc. But the sound is inconsistent. For example, one would think that Rudy Van Gelder's (RVG) "signature sound" - especially during the 60's hay day - would be pretty much the same. I have found that some of his re-engineered, re-mastered stuff is superior to the original recordings on CD; some of the CD's (same title) sound really compressed compared to vinyl, while some can sound nearly analog in presentation ( Wayne Shorter's re-engineered "Speak No Evil" for instance).

What's bothersome sometimes is to go through the track list on-line, then get the product home only to find that it's not very engaging. Guess trial and error ... actual listening tests will have to do.
I grew up in a family of session men, who played on many of the seminal recordings from the 50s. I have a deep collection of albums featuring my family. With that said, the second focus of my collecting has been around Producers.
It is always very cool to see how their sound is adapted to new artists. For example, Glynn Johns produced the Who, the Stones, the Faces and the Eagles in very short order around 1970 to 1973. His production holds up extremely well today. It is a great way to collect.