We present a comprehensive statistical analysis of Swift X-ray light-curves of Gamma-Ray Bursts (GRBs) collecting data from more than 650 GRBs discovered by Swift and other facilities. The unprecedented sample size allows us to constrain the REST FRAME X-ray properties of GRBs from a statistical perspective, with particular reference to intrinsic time scales and the energetics of the different light-curve phases in a common rest-frame 0.3-30 keV energy band. Temporal variability episodes are also studied and their properties constrained. Two fundamental questions drive this effort: i) Does the X-ray emission retain any kind of memoryof the prompt gamma-ray phase? ii) Where is the dividing line between long and short GRB X-ray properties? We show that short GRBs decay faster, are less luminous and less energetic than long GRBs in the X-rays, but are interestingly characterized by similar intrinsic absorption. We furthermore reveal the existence of a number of statistically significant relations that link the X-ray to prompt gamma-ray parameters in long GRBs; short GRBs are outliers of the majority of these 2-parameter relations. However and more importantly, we report on the existence of a universal 3-parameter scaling that links the X-ray and the gamma-ray energy to the prompt spectral peak energy of BOTH long and short GRBs: E_{X,iso}propto E_{gamma,iso}^{1.00pm 0.06}/E_{pk}^{0.60pm 0.10}.
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