TVCs can be considerably more neutral than many active line stages. But not **all** line stages!
A lot depends on how careful the design of the TVC actually is. The issues of TVCs are: bandwidth, hysteresis loss (introducing a loss of low level detail) and ringing (introducing brightness).
The advantage of a TVC is of course no noise and circuit simplicity. If designed properly, ringing attributes can be reduced, but one should note: in order to do this, the TVC has to have a loading resistance that is different for every volume control position. The reason for this is that the TVC must present an amenable load to the sources (DAC, phono preamp etc.) while at the same time being able to change the turns ratio. This is usually accomplished by having the multiple taps of the transformer on the secondary side, selected by the switch. Without an appropriate loading resistor for each position, the TVC will express the inter-winding capacitances rather than the actual turns ratios. Most designers set up an approximate loading resistance, but this ignores the ringing issue, which can only be addressed by a different loading resistor for each tap. With only one loading resistance, the bandwidth and ringing issues will be different with each volume control position. It is likely that many have found that there is a particular volume position that seems to sound the 'best' as a result.
To date I've seen no TVCs that pay attention to this issue. Anyone who has worked with audio transformers will realize how important this is.
Even with proper loading, hysteresis losses inside the core of the device will rob the signal of low level detail in much the same way that push-pull output transformers in a tube amp will (part of the reason SETs have made such a comeback in the last 20 years).
It is a testament to how bad some line stages are that TVCs often outperform them. Circuit simplicity is a good thing in audio (less places for the signal to get messed up) and TVCs are not only simple, but can provide gain and impedance control of the output if designed properly.
Despite this a **properly** designed line section can easily trump the best TVCs. This is a good example of getting what you pay for.