CD Player: Vintage or modern ones?

New cd player is the way to go. 

I have a spare Cambridge 640C, and a Pioneer Elite stashed away while I'm using my OPPO player. Not sure what I'm going to do when they burn out. Probably get a transport and run it through a DAC.

Given you are asking about "old glory" CD players, I am assuming this means you are open to used?  If so I agree there are not many "old" players I would recommend, and they would generally need upgrades / modifications (e.g., the Sony CDP x777es)  But if you are willing to consider "recent" units, there are many, many good options. I would also NEVER recommend buying a new CD player - such plyers decline in value so quickly you really should go used.

With that said, your price range seems to be about $2500-4k based on the units you referenced.  Just looking on the 'gon (with the limitation that it has to be black, which I will never understand either aesthetically or sonically), you can pick up a Mark Levinson No, 512, which was $15k not all that long ago, for $3k, and it would give you perfectly fine sound.  Or on US audio mart, there is an MBL 1531 for under $3k - a very musical CD player. 

Maybe if you give more specifics on what you are looking for, you price range, sound preferences, etc, you can get more tailored advice.  

I used to like thick and warm, lately I’m looking for a balanced, nice punch but airy, realistic and natural, musical one, letting the Diesis Ludos shine, already got a Class A hybrid Amp from them with good body and naturalness, also the R2R La Scala MKII (also with couple of small tubes).

Tastes: Jazz, Bossanova, Soul, Funk, Flamenco, Folk, Classical and Reggae, and when in the mood classic 60/70’s rock.

Thanks for recommendations, gonna have a look!

PS: what is the benefit nowadays using CD’s instead of a nice DAC/Streamer combo?

Look for a  Teak pd-H600 if you want black, incredibly well-built and out performs well above its original MSRP. No bells and whistles just exceptional quality and performance, in a nice size solid package. Arguably The best Teak made.