Difference between 察覺 and 覺察
Although both mean "to become aware of", I feel there is still subtle difference in terms of which action happens first.


觉察 is from 觉 to 察: you suspect something first, then observe some facts that supports the suspicion. For example, 突然教室里很安静，我觉察到原来大家都走了。
察觉 is from 察 to 觉: you observe first, then draw a conclusion about something. For example, 我抬头左右看了一圈，察觉到大家都走了。 


Which one happens first, 察 or 觉, can indicate some difference. Usually we use 察觉 because people often draw conclusions after observing the facts. But when 觉察 is used, the emphasis is on the suspicion or cautiousness.

Note that it is also possible to say


觉而不察: to suspect but not to examine 
察而不觉: to observe the facts but not to realize/understand