I have used both. A few observations in no particular order:
- The Obligato is much more flexible under the fingers. I don't know that this equates to Dominants having more tension, but the composition of the strings makes the Dominant stiffer.
- The softness of the Obligato makes them mostly comfortable and enjoyable to play. Although, the E can be down right flabby -- at least it was on my bass. A hard pizz on the E and it will rattle. You will definitely have to raise your string height a bit to use Obligatos compared to a stiffer steel string.
- The Dominant also has a noticeably smoother, darker tone under the bow. Although both bow fairly well. The Obligato G was a little honky sounding arco on my Shen. As was the D to a lesser extent.
- The stiffer Dominant is also easier to bow IMO. Especially the E and A. The E Obligato tended to get "over-excited" when attempting a forte/fortissimo passage on the E with the stick.
- I was among the unfortunate who had a Dominant break. (D String, IIRC) Fortunately for me it was about shot anyway.
- Neither lasted a particularly long time. I think it is the nature of the Perlon core. Then again, they are not terribly expensive compared to some bass strings.
I tried Pirastro Flat Chromesteel after the Obligatos. They were similar but better. Also, they are all-steel and I have used the same set for more than a year and they still sound pretty good. Actually, they sound better than ever with the bow.
I think I have read here at TB that Jargar is in the category of "gutty" sounding steel strings. I have never tried them. They are not off-the-chart expensive. Might be worth a little more research.