Most drives whether variable torque rated or constant torque rated will come from the factory with a constant V/Hz curve (except HVAC drives). But all that means is that constant torque is AVAILABLE from the motor as it slows down. If you have a variable torque load, it just doesn't ask for as much torque in the slower speeds. The motor is happy to produce less torque than the maximum possible. I have many fans and pumps running with a constant V/Hz curve in the drive and all is well.
The only real motive for picking a squared function (variable torque) V/Hz curve is to save a little (and I mean little) energy on fans and pumps.
Vector drives do produce slightly more torque per amp generally. The real difference is fast response to speed reference changes and better torque at low speeds. Sensorless vector is about as good as flux vector except in applications where cumulative speed error is not tolerable. These would be web processes with tensioning and similar jobs.
As for comparisons with DC motors, you have to be a little careful. A simple V/Hz drive will produce constant motor torque from base speed down to around 5Hz where the performance starts to deteriorate. So, if your application is only in this speed range, you can come very close to duplicating the DC motor. If your application requires constant torque down to near zero speed, you will need a good vector drive and then you will get DC-like performance. If you need full rated torque right at stall, a flux vector drive (with encoder) will be needed with one exception. ABB's Direct Torque Control drive, the ACS800, will also produce full torque at stall without an encoder. If there are other sensorless systems that will do that, I haven't seen them.
A common myth about DC is their speed regulation capabilities. An armature feedback DC system is typically good for 2-3% from no load to full load. DC systems with analog tachs have been claimed to have near zero speed error but, considering that the tachs are spec'ed to be no better than 1% accurate, the speed regulation can't be any better than that. Systems with encoders are very accurate, in fact, so accurate that % really doesn't mean anything. Probably the best way to express encoder error, whether AC or DC, is one pulse plus or minus one pulse, non-cumulative.