There was only ONE big battle? So the sieges of Buda, Peca and a few other major cities don't count as battles? When you capital gets burned to the ground, it generally means you lost a battle...
tlk was talking about field battles, and sieges are not generally considered to be battles. They're sieges.
However your forgetting a fact, if Ogedei never died, the hordes never would have split, so we would have an adaptable Mongolian empire already controlling most of Asia and now trying to get into Europe, and succeeding before the death of the Khan.
Ogodei wasn't immortal, nor was he stupid.
However now Imagine that the Golden Horde owned all of Asia except Siam, India and Southern China. With no instability problems (As they all started after Ogies death) they could field a massive army within months, and army better trained and larger then all of Europe's combined. Now imagine that army tried to invade Europe. Mongolians, who had better tactics, better training and more numbers would win for sure. The victory would come slowly, but until Ogedei's death, I can't image anything stopping the Horde from conquering Germany and Italy.
One big battle which happened to be a great Mongol victory does not constitute better tactics. The Euros would eventually figure out how to beat the Mongols, especially with so many fortresses and cities in the way, not to mention countless natural barriers such as the Alps.
Was Hungary part of the NGC? (I actually don't know)
Were they the most powerful member of the HRE (YES!)
Why would Hungary be part of a Confederation made specifically up of German states?

Anyway, assuming you are correct about Hungary being the most powerful nation in the HRE, that still doesn't change the fact that the Mongols would have to capture countless different fortresses and cities to conquer any sizeable part of Europe.