I don't think anybody explained why there are differences and the difference between the eq types mentioned:
Plug-ins, similar to outboard eqs, can be comprimised depending on the budget of the project and the time the company gave it's employees to finish the project.
In the outboard realm, this could mean cheap parts and subpar assembly procedures. All that has an important role in the way your gear will sound and perform.
In the digital realm (plug ins), eqs can be mathematically comprimised. Also for similar reasons. If they spend more development time on the plug ins, the final cost will increase, perhaps out of the budget range of most consumers.
It's all code based, so if the algorhythms are subpar, then you can imagine how that affects the sound.
Now for the types:
Lin EQ was designed more as a final mix eq. To put it simply:
It's a very transparent eq, but it uses a lot of math to accomplish that. A lot of math means a lot of cpu power.
A lot of cpu power for one plug in means limited amounts of plug ins for your mix. So in the end, it's not a very pratical choice for mixing. Better for mastering or "final mix adjustment" (for lack of a better homerecording termonology).
Also, lin eqs incorporate delay in thier processing, so any track with the lin eq will be offset a good amount (timewise) from the rest.
So if you're going to mix with eq plug ins, better to have something like a renaisannce eq, pultec, joe meekqualizer or focuserite eq. Not the best sound I've ever heard, but very practical.
In terms of "sound", thats more of a psyschoacoustic term. Meaning there's not real measurement for taste. But what I can say is that, I suppose eq plug-ins do well at eqing, but in terms of coloration, I'm not incredibly convinced about huge differences in coloration.
The closest I can think of that "colors" the sound is
the waves Q-Clone, which uses convolution technology. But thats another story.