Kieren you are correct that power/weight ratio plays a factor. But equation for dive acceleration looks like this:
Acceleration = (Weight+Thrust-Drag)/Mass
At really low speeds Drag is not a big issue. So it's basically
Acceleration = (Weight+Thrust)/Mass
However the Thrust/Mass ratio for these planes is much less than 1g, so it's not that much a boost to have a good Thrust/Mass ratio. Most of your acceleration is still coming from gravity.
And in a steep dive, Drag quickly becomes larger than Thrust. Also at higher speeds Thrust is reduced due to prop efficiency. In this regime the Weight is doing a lot more than Thrust to accelerate the plane, and the Thrust/Mass ratio is not an issue.
In the example we are talking about, the Fw 190A did not have a power to weight advantage over all the Spitfires. But it was close. It did have a weight advantage, and about the same amount of drag.
So it might give up a little dive acceleration at low speeds, but it will make that right back up when the amount of Drag starts to exceed Thrust, which happened PDQ in a Fw 190 pointed straight down with the throttle wide open.

There are test reports and a lot of anectdotes that say the Fw 190A would walk away from a 41-43 era Spit in a dive.
[This message has been edited by funked (edited 04-30-2000).]