The "wide and fat" sound of reel 2 reel & FM radio

I had played a jazz cd earlier in the evening....later the same song came on my FM radio station...the FM broadcast sounded "wider and fatter"...I know that is not the proper term in audiophile vernacular, but it's my best description. When I owned a reel to reel 20 years ago, a recording made from vinyl to reel to reel sounded wider and fatter than the vinyl source. Mind you, I bought myself a serious tuner this year...Sansui TU-X1. What is it in reel to reel and an excellent tuner that makes this possible? I'm thinking of buying another reel to reel and make myself some recordings of some of my favorite vinyl.

Preamp..............Audio Research LS-10 solid state (no phono input)
Preamp..............Carver C-19 Tube (I have it connected to the AR LS-10 and use it for a phono preamp)
Speakers............Infinity Kappa 9 (bi-amped)
Amp.................Carver Silver 9-t monoblocks (low pass)
Amp.................Sunfire Signature (high pass)
Phonograph..........Oracle Delphi Mk-I
Cartridge...........Grado Reference Platinum
CD Player...........Carver SDA/360 5 disc changer
Tuner...............Sansui TU-X1
Well, generally FM radio stations are highly EQ'd, especially on the bass, which may contribute alot toward that "wide fat" sound you refer to. As to the vinyl, I don't have an explanation for that.
I have 4 reel decks and a large collection of pre-recorded reels going back to the mid fifties. many of these reels sound better than what "modern technology" would foist upon us. I do see hope for the SACD format, if they'd get the material out.

Buy a reel deck. You'll enjoy tapes you find.
Perhaps the dynamic range is being compressed when you record to tape? This would make the softer sounds more audible, and if those previously softer sounds are more channel specific, you could experience a greater stereo ("wider"?) effect. And perhaps "fatter" comes from any equalization the signal goes through in the tape deck.

If it turns out to be the compression that you like, you might try one of the little dbx compressor/expander boxes to modify the dynamic range when playing vinyl. And as long as I'm disregarding signal quality, perhaps an equalizer could mimic the signal change of the tape deck?
In a similar vein, I've noticed that reel-to-reel copies of some CDs are more euphonic than the source CD. Not a universal phenomonon and I haven't isolated what it is about those CDs that exhibit this behavior.
The effect you describe is called tape compression. Many people do tend to prefer that tape effect over digital...that's why many producers and engineers still prefer to work reel to reel recorders rather than digital, and many more use some combination of the two.

As far as the FM goes...the signal could be compressed, it could be the CD player or turntable they used, etc.