Road.
I've read some people above talk about footpaths designed to accomodate cyclists. Such would be a glorious thing but, alas, where I'm from, they don't exist. Cycle lanes do and they're good but often too small or right on a tiny parking shoulder, meaning that if you ride in them you risk getting door'd. Sounds hilarious but can be deadly.
Anyway, so long as everybody obeys the road rules, cyclists are only going to hold you (you being person in the car) up for a matter of ten to twenty seconds.
On the other hand, if you ride on the footpath, you have to contend with:
1. People stepping out of shop fronts.
2. Generally poor quality pavement (designed for walking, not wheels).
3. People walking dogs.
4. People backing out of driveways.
5. Footpaths suddenly ending.
Really, you need to slow way the hell down to the point where you might as well just jog to work. Which will stop people using bikes. Which will put more cars on the road. Which will lead to more pollution and congestion. Also a less fit populous. Is that really worth it because some drivers can't wait ten seconds to overtake safely?