Power within the Dresden Files is just like real life in that it isn't one thing. One person can be powerful because of money, another because of fame, another because of fighting ability, and another because of firepower. The list goes on.
The Black Court is the strongest of the Houses in pure brute force, and magical capabilities. These qualities made them formidable to be sure, and feared, and hated by many. As strong as they are, they have major flaws.
1. They are deathly vulnerable to things that aren't difficult to obtain.
2. It is virtually impossible for them to blend in with humanity.
3. They are devoid of kindness, honesty, or trustworthiness. They have no real friends or allies.
4. Although they are capable of intelligence, and cunning, it isn't a defining quality of the species.
The White Court is not on their level with regards to brute force, and magical power, but they are very dangerous. As I mentioned earlier, there is more than one route to power. The White Court uses intelligence, guile, misdirection, manipulation, political connections, and wealth.
The White Court could never have faced the Black Court in a head to head fight, but they didn't need to. They took sensitive information about the Black Court's exploits and made it very public. Then all they had to do was sit back and watch as all the people who hated, and feared the Black Court hunted them down.
The White Court brought them down without ever putting themselves into harms way.
A good comparison would be Winter Knight Harry Dresden vs vanilla mortal John Marcone. Sure Harry could absolutely destroy Marcone, but Marcone wouldn't face him directly. He'd have someone pick Harry off from 500 yards with a 50 cal.
So the White Court might be underpowered in some ways vs the Black Court, but who's on the run, hiding, and facing extinction?