Hi peter2727,
Welcome to the forum! And thanks for joining our new family of tape lovers! Your question is a great one, and even before I got into Reel to Reel tape I took my best CD's and transferred them to metal cassette tape on a simple AKAI machine and the playback from cassette was quite a bit better sounding than the CD player even though I didn't know specifically why, I intuitively knew it was the mechanical process of the tape format and the preamp circuit in the Akai that was responsible.. That was in the 1980's and the CD players I used at the time were a top end Denon and a Sony ES player. The Denon was warmer, the Sony had better detail and imaging.
I consider this a fairly extreme example, because you're taking a reasonably sub par source and making it sound considerably better. No loss of detail whatsoever, no veil, no insertion losses, just better sounding playback.
Since that time, and in particular after recently getting into Reel to Reel I've had to learn how they work in an effort to align my machines, which took about a year.
Perhaps the most fascinating part of tape machines is the fact that you can't just lay down a recording on tape with a varying magnetic field of the recording like you would think... instead you have to create an oscillator which works at a high frequency well above the audio band, to assumably excite or break loose and randomize the iron oxide particles on the tape. Picture them all dancing in circles as a result of the strong oscillating magnetic field, and then the music is laid down on top of that determining where the iron oxide particles stop (magnetically point)... which is your recording.
This oscillation has to be adjusted or aligned for each tape head. This alone means that there is a window of adjustment which will effect results.... aka alter the sound signature of the recording either closer or farther away from your intent. This is of course an opportunity for magic to happen (or disaster).
The point to all of this is simply that beyond the flavoring you can get from different types of tape, and different bias settings for those tape types, the osicllation mechanism that drives the ability for the tape head to lay down a recording on tape could well be the illusive missing link to the magic of tape. I believe it is in part capable of re-animating music beyond the actual source.
I have as part of the learning curve I inflicted myself with, figured out how to make all but the very best sounding tapes sound better upon duplication. Turns out there is quite an art to it. You first listen to the recording and assess it's weaknesses. Then you pick a tape formulation that will best serve your intent. After everything is set up you do multiple dry runs where you find the best sounding levels using dynamics as an indicator. You monitor everything you do live in reference grade headphones (not speakers) and as a part of those test runs, which you erase and repeat several times, you adjust the record bias by ear. What happens as you make tiny adjustments in bias, is that you unlock a transparency and immediacy that was not there before. It's a magical experience to hear. By half way through the tape, you'll have the perfect setting of the record bias which will dumb down or excite the actual recording signal. You now have the levels and the record bias adjusted perfectly for the recording so you rewind the tape, and in my case bulk erase the tape on a 19 amp tape eraser to completely remove your test tracks down to as far as I can measure which is -90dB... basically jet black x 2.
I know of no other medium that can do this kind of surgical extraction of the music's intent without penalty because there is no jitter, and absolutely perfect time, no oversampling, no quantization, no smearing, just rock perfect absolute phase across the recording, so far as I can tell from listening to the results and this is what we love about tape, the timing is perfect, even if you raise or lower the speed, i.e.., pitch! This is because timing is relative.
This winter I plan to follow Mr. Pong's lead with custom tube recording chain, and that will make everything I just babbled even more better

So to summarize, with a reel to reel that you can easily adjust (I would recommend the Otari MX-5050 series to start with) the tape bias on, it would be easy to make your best LP's sound better and expand the dynamic range while doing so. Literally, it is like an archeological dig where you find the hidden room with the actual source and can then extract it into reality... music hidden within itself.
-Steve :)