score:5
The actual terms for the three aspects (parivaṭṭa) are:
The aspects for each truth are as follows:
Suffering (dukkha)
The Cause of Suffering (dukkha-samudaya)
The Cessation of Suffering (dukkha-nirodha)
The Path to the Cessation of Suffering (dukkha-nirodha-gāminī paṭipadā)
The realization of the four noble truths in these twelve aspects constitutes the attainment of Buddhahood; it is probably not necessary that a student come to full realization of these things, since they only need to do what needs to be done, rather than fully understand the nature of what they have done. Only fully-enlightened Buddhas understand the truths intuitively enough to teach them; even private-buddhas are not able to teach them to others.
As to their practicality, since they constitute the core of Buddhism, understanding them intellectually is of great importance. It will help ensure that your practice is in line with the Buddha's teaching; especially the first and last truths. The first truth reminds us that our intent is not to run away from suffering but to actually study it, so that we stop clinging to it. The last truth should be studied in detail, to understand all eight aspects of the path.
As to whether they differ between traditions, I doubt the understanding as to what the Buddha taught in his first discourse differs much between the Pali and the Chinese, but the interpretation of what they mean may differ, along with their place in one's practice (since Mahayana seems to see them as only 'relatively' true).
If you're interested, Mahasi Sayadaw's book on the first discourse is interesting:
http://www.buddhanet.net/wheeld01.htm
I wrote a (shorter) piece on them as well:
http://www.sirimangalo.org/teachings/lessons-in-practical-buddhism/simple-truth/