Just boosting the volume will not, by itself, alter the nature of sound. It's only when you
distort the audio that new harmonic and inharmonic components are added that can range from pleasant enrichment to harsh annoyance.
A limiter by nature is a distortion device. Clever designs can mitigate or disguise the distortion, but they all distort and they all add something new to the sound. This is true for both software and analog limiters. The only way to avoid that completely is to not use a limiter at all.
The difference between digital and analog devices is that digital processes can only mimic the way analog amplifiers naturally saturate. You have to really drive a vacuum tube hard before the distortion becomes unpleasant, and as it transitions into unpleasantness it does so in a gradual way. With digital devices, the onset of unpleasantness is abrupt and profound.
Another difference is that analog devices are simpler, with fewer options. They're easier to understand and use, and more difficult to abuse. Digital equivalents tend to offer many options, some of which are dangerous. A tube device will be designed to not react fast enough to do the worst kind of damage. But software can react to individual samples if you tell it to. At 44.1 KHz, that's about 50 times faster than the threshold at which you're likely to start causing audible distortion.
So when I hear somebody say they get much better results with outboard gear, my first thought is that they were probably mis-using their digital gear in the first place.