Thats a tough one. As far as which is more "cutting", I might have to say Chromes when new because they just have this weird metallic thing going on that never bothered me for years, but recently I cant stand them. TI's Jazz Flats are bright though, but seem less "meaty" than Chromes. TI's have a lot of sustain, too, and are very musical. Chromes have a lot of sustain, but maybe a little less than TI's, and although they also are musical, they will get a little "deader" sounding over time and lose that high end zing.
Also keep in mind the tension of both sets. TI's may require you to change your attack and/or action because they are so low tension, if you have a heavy right hand they may flub out for you. Only reason I have them on a bass is I prefer flats, but the particular bass they are on has a neck that doesn't seem to like higher tension flats and I had to keep cranking the truss rod on that bass, so I threw on some TI Jazz Flats and had to back off on the truss rod quite a bit and the bass is much happier now! Not my favorite string, but it's a nice change from the other flats I have on my P's.