Yes they are directly related.

For yield, no. Not in awhile.

For performance, I can tell you out of Nicehash, Winminer, & Minergate that Winminer is currently the least stable. Let me be clear that Winminer is my favorite of the 3, but it is unfortunately very buggy.

I use Minergate on some of my low end systems with AMD GPU's since it is the most productive with those setups. Many people say that Minergate "steals" hashrate from you. I don't know if they are, but it is more productive than Nicehash or Winminer on those particular machines because it uses the GPU that they won't. I can say that Minergate by far is the most stable software though. I have machines that have run Minergate for weeks without a single reboot or crash. Actually I don't think I've seen Minergate crash EVER, and remember I only use it on my most crappy hardware.

I use Nicehash on my more powerful machines that I can't babysit daily. It seems to produce about the same as Winminer after all is said and done, but I have not done a thorough test. But anecdotally I can say they are very close. Like I said I only use it on machines that I can't get to everyday, and it does crash now and then. But it picks up where it left off after a reboot, so I can "set it and forget it" and generally not lose more than 12 hours, even after a crash.

As for Winminer, it is my favorite and I am behind them 100%, but man oh man the bugs are frustrating. Across about 30 machines that are about as diverse as they can be Winminer crashes ALLOT. On many of my machines it crashes multiple times daily. And something in the last 4 or 5 updates (that all came out in the last two days) is really messing up my 1070 and 1080 machines. 2 or 3 now won't GPU mine at all since they get an "ethminer has stopped working" crash over and over again. Much worse is that after after a crash, Winminer often "forgets" all its settings, so even if I have it set to autorun after a reboot, it won't start mining until I re-enter all the setup details. I lost *days* of mining on some of my machines due to this, which is why I had to go back to Nicehash with them. I've seen several other people complain about this same issue on various forums so I am sure their support is aware of it.

Again, Winminer is my favorite, even with the bugs, and I expect they will all get sorted sooner or later.