I'm planning on using radar to count car traffic on a slow speed road. What I'm wondering is if I should expect doppler radar to be good enough to get an accurate count? Alternatively I could also use FMCW radar in addition. Will adding FMCW give me much added benefit over just doppler?
Your problem "counting traffic" is essentially a target tracking problem: just seeing the speeds of targets reflecting, or their distance, or both, will not allow you to count cars; you will need to be able to track whether something is a new car or just the same care as in the last radar estimate, moved a bit further.
This can be done on dopplers alone. Of course, theory tells us the more useful data we have, the better we can estimate, but seeing that cars probably don't change speed drastically between two radar periods (which probably are less than milliseconds apart), a simple "gating" filter (observe something with a given doppler the first time, calculate a sensible upper and lower deviation from that doppler, and if that is hit, assume it's the same car, if not, add a new car to your tracking).
What's bad about doppler-only is that you won't be able to track two cars driving at the same speed with little distance; that's something you'll see quite commonly in a slow-speed street.