So the new iPad has an A5X CPU and iPad 2 has an A5, new iPad has a better battery than iPad 2 and the cameras and screen of the new iPad are better than the iPad 2 but other than that it doesn't seem very different to the iPad 2.
The screen and cameras aren't factors of whether Siri would work or not so they can be discounted. That just leaves the CPU and battery to consider. The A5X having a different architecture (that I'm assuming otherwise there is no point in developing it) and is probably faster and capable of handling more instructions at any given time than the A5 but Apple have already proved that the A5 is more than capable of handling Siri with the iPhone 4S.
The new iPad has a 42.5-watt-hour battery and the iPad 2 has a 25-watt-hour battery. This is a very large difference I'll admit, but the iPhone 4S has a 5.3-watt-hour battery so 25-watt-hour is more than capable of handling Siri also.
So I stick to my original statement that the iPad 2 is more than capable of handling Siri