I've tried a few synths and like a couple of them a lot. The Muhle STF v2 is comfortable, not too springy and whips up a nice lather. The Razorock synth knots are also very efficient. However, I wouldn't compare them to badger knots (which differ widely in any case) because they're just not the same beast. Badger knots just have that element of a bit of scritch and individuality that synths lack, for me.
I can't ever recall feeling a badger. Very shy creatures too, so pretty difficult to do so I imagine.
On a more honest note I really don't get on with natural brushes so from my angle I see a good synthetic as a betterment more than a 'close' replicant.
Out of those I do have I find the Razorock 400 to be a better (and easier to use) performer than either of the two Muhle Silvertip fibre brushes in the cupboard. The Muhle brushes are fine but just seem to lack that body about them. The 400 is just one lather monster in comparison.
RazoRock Plissoft 24mm, RazoRock Disrupter 22mm, or (especially) the RazoRock BC 24mm Silvertip. Having used one Badger and some Semogue boars (which are good), I now find these are the brushes I use regularly. They lather very well and give great performance.
I've never used a synthetic that I thought felt like a badger. My favourites are the cashmere and tuxedo from APShaveco but I can't honestly say that they feel like a badger.
I've yet to find one. But it's like comparing a boar to a badger or a horse to a badger. Each has its own distinctive feel, pluses and minuses. At the moment my favoured synthetic is the AP Shaving Synbad, but I use it only for travel because it dries very quickly unlike my boars and badgers. It makes tolerably good lather, but its on my face performance and feel is no match for my quality badgers and boars.