From: Achromatic | #047
Uh, Minato will absolutely kill an opponent without mercy if he has to. Like I think the only time Minato is shown taking it at all easy is during a recent flashback because he liked a ninja and there was no need to escalate the situation. Minato is a stone cold killer, and there are thousands of body bags to prove that.
Well, even if Yusuke does talk at the beginning, I still see nothing that could kill Yusuke. Kunai's I'm convinced would do nothing to Yusuke, just because of the bit he had with Sniper. If he did happen to get behind Yusuke, I'm pretty damn sure Yusuke could easily counter.
Yusuke can play it reckless and arrogantly and still survive. Minato has shown me nothing that he can compete with Human Yusuke, because you also have to remember that technically speaking, he was still training his human side too for those 3 years before the demon tournament.
Essentially I'm saying is that the best opponent we have seen Minato beat is A(Raikage? I don't really remember early Minato scenes), and well, he just doesn't compare to anyone in YYH. We haven't seen some super strong super bad guys that Minato has defeated, while in YYH we have seen that, so we have to base it off his techniques, and while good ones, I just don't think he has enough to beat Yusuke.
Edit: Unless you want to count Madara....but, that really wasn't a 'fight'.