Quantity and quality both are important. But if I have to choose I will take quantity. Look at WW2, the Germans made AMAZING tanks, but the Allies still beat them because they made TWENTY Sherman tanks for every Tiger tank made. Also, Zerg Rush. Look it up and you will understand
America is fighting small scale conflicts oversea, And quality is always better than quantity for small sized wars. Here's why: you can only commit limited amount of assets into a small war zone. If that is the case, Then you want those assets to be as high quality as possible.
With nuclear weaponry in mind, There will unlikely to be full-scale world wars during which quantity trumps quality. Committing a large quantity of troops will escalate the small wars into big ones, Which can result in Nuclear exchange.
The biggest conflict you will ever get in the future will be the size of Gulf war, During which the superior quality of American troops trumped the numerical advantage of the Iraqi forces.