Somewhat agree with everyone else ..
Was very very happy with my lathe 1.5 kW industrial AC (EU, 220V single phase) motor and belt drive for 8+ years.
Had VFD on my Bridgeport M Head and thought it was excellent.
Then built a good rigid industrial timing belt drive for the lathe spindle, HTD-8, 30 mm wide.
1:3 transmission, 24 : 72 teeth with industrial tapered bushings.
With a goal of a C axis for milling, cnc.
And a 2.5 kW industrial AC brushless servo, 10 Nm cont, 30 Nm peak.
So 90 Nm peak torque upto 3 secs.
The end result is absolutely unbelievably good --
because of the absolutely constant steady torque and feed,
absolutely perfect surface finish,
10x the effective torque EVER before in high-load situations at low rpm,
From 1 rpm to 1000 rpm.
So I have used 25 and 30 mm drills in tool steels, 50 mm deep, using 2-4 kW of absorbed power, with excellent results.
About 3x faster than the old system, and with no belt changes, and no backgear.
And an ISO BT30 face mill, 50 mm wide, cutting 4 mm deep into a tool steel block at 600-700 rpm, medium high feed, fantastic finish.
About 7x faster than ever before.
The AC servo is vastly better than I ever expected, and mostly due to the torque.
Which I did not expect to be important at all.
And also because when it stalls, the machine stops, and nothing breaks.
The error count reaches a certain number, around 0.02 mm in positional error, and everything stops no-muss, without breaking tools, mounts or drive axel bearings (built very strong, industrial).
Even very thick/big workpieces and tools easily bend over 0.02 mm (to 0.1 mm, maybe 0.2 mm) before breaking or breaking their holders or mounts.
I´ve stalled the spindle drive maybe 4 times, and this is no problem.
Overloading it, effectively using 7.5 kW of power or more for 3 secs or more.
A modern good VFD is functionally and electrically very close to an ac brushless servo.
They both have about the same parameters in terms of pid tuning, and do ramped acc/dcc and reverses and adjustable speeds etc.
Anecdote..
A 2.5 kW AC brushless servo, here in europe, 220V household current,
will accelerate to 3000 rpm in about 10-20 ms, or 0.02 s.
No load.
A VFD accelerates a 3 kW motor in about (0.5)-2 secs.
It could do better, but would typically overheat or overload, say if run 1000 times continually fwd/rev at max acceleration.
The servo reacts about 100x faster than a std motor/vfd and updates the reaction parameters at typically 12 kHz or 0.0008 secs.