DACs only purpose is to convert the digital signal into an analogue form with as little distortion, noise, jitter and other nasty artifacts as possible. A few other things, but you get the idea.
R2R and Sigma Delta take quite different approaches to doing this. Quite different technologies.
R2R DACs do not do this as well as SD DACs. R2R DACs such as those by Denefrips and Holo Audi can come very close to what most robust (and recent - technology has improved in just the last couple years or so) SD DACs can easily achieve.
Now, R2R DACs do convey perhaps a slightly more lush/euphonic (whatever, get out the thesaurus) presence than SD.
The reasons to me are unclear, however one reason that I a familiar with is that R2R DACs introduce 2nd and 3rd harmonics through into the signal. Perhaps google is your friend for an explanation of harmonics.
These are known as non-linear distortions. These can be very pleasant to the ear, and tube amps produce them (harmonics) in abundance. Many here enjoy tube amps, myself included. {edit - and now I see, yourself also. Swell}
My own opinion is that should you wish to introduce such harmonics the best place to do so is at the pre-amp or amp level.
Get the source signal as "correct" as possible with a SD DAC costing no more than a few hundred bucks, and then decide how to play with or customize the signal that the DAC spits out.
{I see Schiit has been recommended. If that is a brand you trust, I'd suggest Schiit Modius at $200 - it is splendid and you won't be disappointed. Jason from Schiit would agree - he has said that he can't tell the difference between DACs after a few beers, which, I may note, is because they are so good these days and is probably true even before having a few beers}