Apart from 働く being a verb, and 仕事 being a (suru) noun, what is the difference between the two?
They(仕事する and 働く) mean "to work in a company or as a one-person operation" and also "to do something".
However 働く has some meanings besides like 作用する(act on). For example, 地球では重力が働く(Gravity acts on the earth) http://dictionary.goo.ne.jp/jn/176758/meaning/m0u/%E5%83%8D%E3%81%8F/
Putting parts of speech problem aside, 働く stands for "labor", the activity you put some effort to do something, while 仕事 is "job", or what you put your effort to do. Both are common words and applicable when you describe people working at office.
It's not so easy to find situations only either one makes sense because the two are usually pairing up, but for example:
百人力 means "100-people worth of power" or "Herculean strength" (not Herculean task) to express how you are efficient to get works over with. It can only modify 働き and not 仕事, because the job is the same job.
急 means "sudden, urgent". What comes suddenly isn't your performance but the task.
Below listed some extra definitions each word particularly have, for your information:
- 働く: to commit (a crime), to function
- 働き: function, performance
- 仕事: profession, work (of physics)
As you see the Japanese word "働く" consists of the Chinese character "働" and Japanese character, Hiragana "く." On the other hand, "仕事" consists of two Chinese characters. You can almost always use both words for the same situation.
"I hate working on Sundays."
Correct: "日曜日に仕事するのは嫌だ", "日曜日の仕事は嫌だ"
However there is a slight difference between the two words. A word consisting of a Chinese character and a Japanese character Hiragana gives us a soft impression. So if you give a title for the TV program for children about the vehicles like cement mixer truck, Fire Truck, Police Car and Ambulance, etc. In this case "働くくるま" is a little bit better than "仕事のくるま." There is almost slight difference but when you come right down to it "働く" is rather casual and "仕事" is rather formal.