Nope, dual core 800Mhz does not equal 1600Mhz performance. It doesn't work that way. Dual core means that you have 2 processors doing different things at the same time, or the helping each other doing something at the same time. Each processor has a limit of how many things it can do at a time, called instructions threads. For the sake of simplification, lets say each processor can handle one thing at a time, and the difference is speed. A 1Ghz can do task A in 1 sec, while an 800Mhz processor can do the same thing in 1.2sec. This means that while it will take a single core 1Ghz processor to do task A twice in 2secs, a dual core 800Mhz can do task A twice in 1.2 secs, because you have 2 processors running doing the task at the same time.
Now the example I gave is an oversimplification and this doesn't take into account the processor generations. For example, a dual core Exynos 5 with A15 chips (Nexus 10) is as fast as a quad core Exynos 4 with A9 chips (Galaxy Note 10.1) because the newer A15 chips can handle as many tasks as two A9 chips (again oversimplification). But the gist is simple, if you are looking at phones, and wondering about possible performance, look at processor generation, then number of cores.
An easy answer to the question is that a dual core 800Mhz would be better and faster. I'd suggest looking at a Galaxy Ace 2 at your price range, or an Xperia Sola.