In response to the question you posed, they don't. Much like a boar doesn't compare to a good badger, the same goes for synthetic, horse, mixed knots and whatever else you want to try and lather with. The fact is that all fibers/bristles have their own unique characteristics and will perform differently based on such. I have tried Gen 1,3 and 4 synthetic brushes and they have come a long way in softness, water retention and resiliency. However, they have a long way to go before I consider them a good replacement for my favorite badger brushes.
I beg to differ. I would say much like a good boar doesn't compare to a good badger. I no longer own a badger brush. I always reached for my Semogue Boars and may never own a badger again. With that said, I will have my first foray into the synthetic market tomorrow with a new Muhle Black Fiber. If I enjoy it, I will go for one of the higher end synthetics.
... IMO, the only ones worth trying are the Muhle brushes. They are just better in every respect than the other synthetics...
After a month long use of each brush, and they all had their pluses and minuses, my Synthetics of choice were the Pur-Tech & TGN.
Oh, TGN? Are they gen 4?
The story of my life - late to the party - again...
I just bought it last week, don't know for sure but it's about dead even with the Pur-Tech I bought last month. The TGN is the 23 mm knot, it has a glue bump which reduces the lof ~10-12mm and they call it a three-band; http://thegoldennib.com/index.php?main_page=product_info&cPath=9_89&products_id=760
Synthetics, for me, are the way to go. I agree with blzrfn that each bristle type has its own characteristics, so comparing boar, badger and synthetic is a little bit apples to oranges. But my favorite brush, and the only one I'd need, is my Muhle silvertip fibre. And I'm not even sure whether it's v1 or v2. It just lathers like a monster and requires nothing more than a rinse when I'm done. I also like my somewhat softer muhle black fibre. Event though it was less expensive, I don't think it's any less a brush. Softer and a bit floppier than the STF.