Well, it's like this in the Realtek versus Intel(and Broadcom's are pretty good too apparently).
1. The CPU does
all of the heavy lifting with Realteks. Intel's do most of the hard work on-chip. This doesn't matter if you have a 24 core system. But for those of us trying to make do with less than outrageously expensive hardware, you are going to have a hard time getting full 1Gb speeds from Realteks. Most people hit about 650Mb/sec max with Realtek. Go to Intel and instant 850Mb/sec+. Not to mention their driver is single threaded, so expect horrible performance with Intel Atoms and other "Green"(and old) CPUs. The more powerful the system the less improvement you'll see with Intel. But really, who cares? Intel's just work!
2. Intel has spent far more money to give great performance with low CPU utilization where Realtek is meant to be cheap so that they can make money off of the high quantity of network chips they sell.
3. Realtek doesn't really support their non-Windows driver, so they're written by programmers that have less than nice things to say about their hardware.
If you want a good laugh, check out the programmers comments from prior versions here.
4. Plenty of people have had very bizaare performance and reliability issues with their network gear. No explanation can be found and they're beat their head into the walls until they give up. The buy an Intel NIC from ebay, and suddenly all of their weird issues are instantly gone.
Personally, I had performance issues between my server and desktop at home in 2008. I was a single user and very unhappy with the very poor network performance I was getting. 50MB/sec max for a single user when the hardware could do over 700MB/sec with its RAID array was disappointing. I tried tweaking the system registry and all sorts of stuff. Nothing really worked despite weeks of trying everything. Lots of people swore off Realtek and praised Intel, but I didn't see a point since 1Gb should mean 1Gb, right? Wrong. As soon as I replaced the Realteks in my server and desktop with Intels I got 100MB/sec. At that moment I swore off Realtek and I've never gone back.
In 2012 when I started getting involved with non-Windows stuff(mostly Linux Mint and FreeNAS) everyone said the same thing. If only I had known that a few Intel NICs would have mattered that much i would have started using them years before. But basically, when I go looking for new hardware, I always either go with Intel onboard or get an Intel NIC. I keep 2 spare Intel NICs around the house too just in case I need one for someone's computer. And for their price its kind of hard to say no considering how much performance improves by using them.
So yeah, basically those that are more seasoned will tell you Intel is just the shiznit. Less seasoned users might just dismiss potential limitations of their network as a bottleneck from somewhere else. But by far and large, the vast majority of "network problems" threads created in this forum are solved just by getting an Intel NIC. It's quite depressing because the forum is full of threads, most of which have the exact same solution. If people would just read and spend the $20 for an Intel NIC they could have saved themself a lot of time and the forum from "yet another non-Intel user that couldn't listen". :P