Basically they got the same meaning ,u can use either of them or both of them at the same time as well,for example, 我正在思考这件事， 我正在思考着这件事， 我思考着这件事 but using 正在 would be more emphasize the action is happening

thanks Jeff

i am making a mandarin course recently. 了 着 过 have been put into the same group. they are all used following a verb. "verb+了" is similar with "done" in english. "verb+着" is similar with "doing"... "verb+过" is similar with "have done "... there is a close relationship betweem the word(了,着or过) and the verb.they constitute the whole. but 正在 is different. it just a general adjective to describe the state of the moving compared to 着. another 2 words are put in the same group with 正在 in my course. 已经, means a movement already done 还没, means it's a negative. the movement didn't finish 正在, the movement happening hope it helps

yes there are certain emphasis in both ways. when you use 正在+ verb It implies that your doing which is being discussed is still in progress. ex: ---Why hasn't he brushed his teeth ? He's almost late. ---Oh, yes, he is. 他正在刷牙。 On the other hand, using "verb+着" is an expression to describe a state. ex: --- What's he doing now? I can't find him. ---He's brushing his teeth in the bathroom. 他刷着牙呢。

Thanks Colin