Is directing air traffic similar to directing street traffic?

Yes it is but with addition to vertical clearances. Road traffic is considered as 2 dimensional where air traffic is 3 dimensional.

They are not comparable at all. An air traffic controller does just that. He controls the aircraft traffic in his assigned area. Whether they are just passing (transitioning) through or they are going to land your airport location. You help with collision avoidance, spacing, headings and altitude. Depending on where you work or what level you are will dictate how stressful you job will be.

Hello Mae,
The two careers are very different and not very comparable.
Air traffic control works 3 dimensionally, you are controlling the altitude, direction and speed of multiple aircraft. Also you are in constant communication with each of those aircraft while they are in your section of airspace. Sometimes the pilots do not speak your language and it make it more interesting. When emergencies happen, you have to shift focus on that particular aircraft and get it down safely and expediently without neglecting all the others. Not to mention that each aircraft can have a few hundred lives depending on you. It is a very stressful position, especially since you can't ask them to pull over on the next cloud and wait for the next light. Your work environment is a room filled with many other controller and staring at a radar screen waiting for the next bleep to pop on your screen and make radio contact.
I think street traffic is considerably less stressful, since you can stop everyone, hand signals are pretty much universal, and worst case scenario you get a fender bender. If you make a mistake here, usually everyone lives.
Hope this helps, good luck.