Well, I'll give it a try...
I do have a bass with TIJF's on it, and one that wears TIJRs. But, the Jazz Flats are long scales on an Alembic Epic, and the Jazz Rounds are short scales on a hollow-body Gretsch Broadkaster. So, apples to apples it ain't...Anyway, here goes;
- TIJF's. Low tension (143 lbs.), extremely flexible due to their "orchestral string" construction. What some call "round wound quality" is their heavy focus on the mid range. Low end is... adequate; their low-mids are... good. Mid-range and high end, is where they really shine. and, their construction gives them harmonics that most other flats can't touch. I have them on an Alembic Epic, which I use strictly for Jazz. In that role? They are simply superb. But, for most of the other music I play? Uhh... not so much. For me, TIJF's are pretty much a One Trick Pony. Lots of others disagree, but after playing lots of different flats for 50+ years? I know what works for what, pretty well - for me...
- TIJR's. They're also low tension - for rounds; but, I can't give you any numbers. Short scale strings - on a normal short scale bass, tend to get a little... limp... as the gauge gets lighter;and, the TIJR's are pretty light gauge. But, because the Broadkaster is very big for a short scale bass - and these strings just barely fit - they're probably stiffer than they would be, normally. Stiff enough that I can play them with a pick, without major technique adjustments, anyway.
So, how do they sound? On the Gretsch, they sound like... well, pretty much like Jazz Flats, but just a little more "bright". Trying to think of other rounds to compare them to, but... I've hardly ever played anything but flats and tapes, so my experience with rounds is... skimpy, at best. Actually, the closest I can come, is the old Rickenbacker Light Gauge Nickel Rounds. 42-97 gauge, IIRC. On my 4001, I liked them an awful lot. They were bright, without being "twangy". Actually, the more I think about it, they did sound a lot like the TIJR's...
So, bottom line? TIJF's are fairly bright, mid range-focused flats. TIJR's? Slightly brighter TIJF's, that are a little less smooth, and don't last quite as long...