Let's set apart all pros/cons of chains vs belts, like: ease of maintenance, need of a custom frame, cost, spare part availability, all of that: nope. This question is very focusing only on performance.
I read several reviews, one the most interesting being this one. They measure the performance of the two systems with this tool:
and they come out concluding that:
a conventional chain drive consumes 2.92 watts on average, while the belt eats up 3.93 watts. Although the difference is just 1 watt – not enough for most people to care – this works out as a substantial 34.6 percent.
But unfortunately, also:
That data does have some caveats, though. While the chain drive was tensioned to a typical 2lb, Gates recommends a much higher preload tension of 85lb in order to prevent slippage under load.
So, overall it is to be expected that the old chain is going to be more efficient, according to that. But let's not forget that the belt drive system, though less efficient, is also way lighter!
This also affects performance.
In fact, to this article shows how "the entire belt drive system consisting of a belt and front and rear sprockets weighs nearly half of a standard chain", which is a massive improvement in weight.
So in short: Would the weight gain compensate for the performance loss?