I don't know Corelli strings, but I used EP Regular and Weich for the last few years, and before that used SFs for many, many years, before discovering Flexocor Deluxe.
FDs:
On my bass (60's German gamba bass), the FDs are hands down the better arco string, followed the SFs (both are "rope core" design). They start right away under the bow and produce a clear, expressive, bell-like tone. I'm also getting a very nice low end. I don't know the specs, but the FDs subjectively feel thinner in diameter but tighter than even the EP Weich. With my bass, this works out nicely. And I actually prefer the FD pizz sound to any other string I've used (including Spiros).
EPs:
I loved the warm, burnished sound of the EPs (both arco & pizz). They made my bass sound like a much older instrument with some pedigree, but ultimately they tended to wear me out (something which is not happening with the FDs). Also, I feel that that very nice "toasted muffin" tone comes with a cost, because ultimately the pitch definition was too blunted for my tastes. Both FDs and SFs produce a clearer, more defined pitch on my bass.
SFs:
Once upon a time (when there were far less string choices out there), the SFs worked real well as a hybrid do-it-all string and a valid alternative to Spiros for playing jazz.
It's been a while, but as I remember them, they required a pretty long break-in period to tone down their brightness. The FDs are a similar design, and I did go through a weird 2 week break-in period (reported by others on TB ... *** happened to the sound???), but after they got over that, they remain a powerful, intoxicating string to play. And I think you'll be able to play more than "a little" jazz with them.