Couldnt say whether TTs give a better cut or not as a consequence of design parameters, probably not and likely no difference between a TT and a well ground and set conventional tool for finish.
In my experience, the utility and cutting qualities of TT come form the fact they are dead easy to grind correctly and keep razor sharp (by using a simple jig and a wipe across a sanding disk). They are also easy to set correctly and to height, compared to having to pack into a conventional toolpost (not having the usual 40 or 50 QCTP holders that most people seem to have).
For those of us without a toolcutter and who have to rely on some dubious grinder offering from the local DIY store TTs are a great benefit, you can always have a sharp tool in seconds with minimum effort.
I have ground (or attempted to grind) function specific tools ‘like wot they show you in the books’, but found it far from trivial. More often than not, after hours of reducing expensive HSS to a carpet of abrasive dust all over the workshop, I am rewarded with a multi faceted horror, of doubtful cutting quality. Come the time to re-sharpen said horror, repeating the angles never seems to go well, and using a slip stone is not satisfactory either (before anyone shouts out). And then it all has to be packed up to height again because the dimensions change as you cut back the edges of angled surfaces, etc.
Thing is, you can get away with a less then perfect tool for ‘yer bog basic steels etc, but the truth about the shoddy condition of your cutting edges can suddenly and unpleasantly be revealed when you come to hack away at something a bit tougher, PB or SS for example. This is where a TT can make life easy.
The TT is not a universal panacea, just a very useful go to cutter in the dilettante’s workshop. One of the best returns on time and effort to make I have experienced.