Inverters that produce sine waves are better than those that produce other waveshapes, like square or "modified sine". For a discusion of this, see this question.
In this sense, the "quality" of the signal can be measured by its harmonic content. Ideally, the waveform is a pure sine in phase with the power line and has 0 harmonic content. The power industry has converged on another way of expressing what amounts to the same thing, which is the power factor. This measures the fraction of the overall voltage that is in phase with the power line. A power factor of 1 is therefore ideal. A power factor of 97% or higher is quite good for most purposes, and needs to be reasonably sinusoidal to acheive that.
There is no reason for you to care how a particular inverter achieves low harmonic content or a high power factor, only that it does. Some inverters, probably in fact most of them that produce sine output, have a DSP (digital signal processor) inside controlling the power supply to keep the output sinusoidal. The only difference in this case is that the marketing literature mentions it.
So to recap: First, most inverters with sine wave outputs will have a DSP inside. Second, it doesn't matter anway. All you care about is that the power factor is high enough, or conversely, the harmonic content is low enough. How that is achieved internally is irrelevant to you.