What is more important for speed: Processor Speed or RAM?
Your question as asked unfortunately has no proper answer. The only way to answer it is to do as the previous responders have done and assume a larger context.
I don't know why it is that people in general cannot grasp that computer performance can never be quantified by focusing on just one or two components. Computer performance always depends on the performance of the system as a whole.
Here are some of my thoughts as I read your question. (Many have been previously mentioned and I apologize for the repetition. It struck me it might be worthwhile to consolidate them).
CPU clock speed only matters when comparing otherwise essentially identical processors. The amount of "work" performed per clock cycle is much different between, say, a Pentium 4 and a Core 2 Duo because their internal architectures are different.
What CPUs are you comparing?
The CPU to RAM throughput also is extremely important. An ostensibly faster CPU which is constantly waiting on RAM will appear to be slower. An Intel CPU with a high clock rate but an 800MHz Front Side Bus (FSB) may well run slower than a one with a lower clock rate but faster FSB.
How fast is the connection between your CPU and your RAM in both cases?
For similar reasons, the throughput between the RAM and the hard drive can also have a significant impact on system performance. This is after all why folks will pay the still exorbitant premium for a Solid State Drive (SSD). A fast CPU using a hard drive only a few years old will be slower than one using the more recent higher bit density platters.
After a certain point, the amount of RAM installed is only beneficial to the extent the operating system used and the applications run are capable of effectively exploiting it. I recently increased the RAM in my Win 7 64-bit desktop from 4 to 6 GiB. I did not see any noticeable performance increase. The extra memory is most likely just not being used because of the way I use my desktop.
One cannot compare DDR2 to DDR3 without any context. A naive answer to the question as you asked might be misleading depending on the full system context.
By the way, since all recent motherboads support dual (or even triple) channel access you should never install only a single stick of RAM. Instead use match pairs. Using 2 x 1GB of DDR3 or 2 x 2GB of DDR2 will give you better performance than a single, larger stick of either RAM type.
FSB bandwidth, if you don't have any specific applications in mind.
As Ignacio said, it depends on what application you're doing? Are you doing video editing and processing or working with spreadsheets or playing games.
Also, the specific processor models make a difference. You can't compare in terms of raw clock cycle the performance of a AMD processor to an Intel processor or even a Core 2 Duo to a new Core i7.
However, in general more most people, I would think 4 GB of ram with 3.7 Ghz is better than 2.7 Ghz with 8 GB of RAM for pure speed. And DDR3 may be faster than DDR2 but SPECIFICS matter.