Randy, That's the wrong way round: It's rated torque up to rated speed for the VFD, rated power above rated speed.
VFDs vary the Voltage with the Frequency. Below rated speed, the Voltage is reduced (usually proportionally).
Oversimplifying by ignoring losses: Power is Volts times Amps. Amps vary with Torque so for constant torque, Amps are constant.
Power therefore varies with Voltage, just as in the case of the DC motor.
With the DC motor, once Voltage (and therefore speed) is at the rated value, there is no more to be had (increasing them further would subject the motor to excessive Voltage).
Where the AC system wins is that the VFD can continue to increase the Frequency whilst holding the Voltage at the rated (safe) value. Volts times Amps does not increase, so Power is constant, but the frequency can (usually) be increased to "about" twice the rated value without serious electrical issues SO LONG AS THE MECHANICAL COMPONENTS CAN HANDLE IT SAFELY.
Most standard industrial motors are effectively designed as 2-pole motors for 60 Hz supplies, since this is the highest-speed standard configuration (3600 RPM synchronous speed). Much of the rest of the world runs on 50 Hz, which would run the same motor at 3000 RPM. The bits that make an motor 2pole, 4-pole, etc. are the windings which are in the static casing of the motor and are not subject to stresses as a result of the speed of rotation. It is therefore no problem for a motor manufacturer to put multipole windings in a motor casing that can handle the stresses of a 2-pole configuration.
Early VFDs could usually run standard industrial motors between "about" 10 Hz and "about" 100 Hz quite happily and the usual recommendation was to use a 4-pole motor (around 1800 RPM at 60 Hz) between 10 Hz and 100 Hz for a 10:1 speed range. At the time I first played with VFDs, (late 1980s?), DC motors and drives could run speed ranges of around 50:1.
Very-high-end drives which use external feedback systems to measure the rotating speed of the machine they are running have long been able to achieve 1000:1 speed ranges and are found in both AC and DC variants. They tend to be properly spendy.
As electronics have improved, Sensorless (Flux) Vector drives have become more common, with SV now being a feature of most of the newer entry-level drives. SV is a system that allows the VFD to measure the phase angle between peak Voltage and peak Current internally. From this, it can make on-the-fly adjustments to the Voltage to keep the angle at the specified value for the motor. The parameter entered at setup is the Cosine of the angle, also known as the Power Factor. The bottom end of the speed range is significantly improved and SV drives can match DC drives for speed range: 100:1 or better is my experience.
Whilst there was probably some truth to the "DC motors have a lot more torque at low speed" 30 years ago, by 15 years ago it will have been "DC motors have a bit more torque at very low speeds" and now it's probably fair to say that there is no discernable difference in performance.