Don't just look at the MHz; also look at the latency. The "true" speed of a stick of RAM, in simple terms, is the clock speed in MHz divided by the latency.
So a stick of 2133 RAM with 10 latency (pretty common) will give you a relative speed of 2133/10 or 213.3. A set of 1600 MHz RAM at 7 latency (for example this http://www.newegg.com/Product/Product.aspx?Item=N82E16820231628) would give you 1600/7 or 228.6, which would actually be slightly better. DDR3-2800 sounds like a big step up, but at 12 latency it'd give you 233.3, which is not as much as you'd think.
The point is: While faster clock speed generally means faster overall, two sets of RAM with identical clock speeds can be quite difference. So don't just look at 1866 or 2133 RAM and grab any old one; pay attention.
As clock speeds go up, latency tends to go up also - and at the high clock speeds, voltages increase as well. So that set of DDR3-1600 at 7 latency can get by at 1.5V, which is the standard for DDR3, while most of the RAM with speeds in the high 2000s will use 1.65V. That's not the end of the world for a DDR3 machine, but you are more likely to run into compatibility issues such as the motherboard not knowing what to do with it on "auto" settings, etc. One more thing to be aware of.