We have employed a reliable technique of classification of AGN based on the fit of their spectral energy distributions with a complete set of AGN types and starburst galaxy templates. We apply this method to a sample of 116 AGN selected for their X-ray and mid-infrared emissions in the extended Groth strip (96 with single detections and 20 with double optical counterparts). With this technique, we are able to obtain photometric redshifts and to distinguish between pure and host-dominated AGN. For the objects with unique detection we find that they can be separated into five main groups, namely: Pure Starbursts (24% of the sample), AGN contaminated by Starbursts (7%), Type-1 AGN (21%), Type-2 AGN (24%), and Ellipticals & Spirals (24%). We find these groups concentrated at different redshifts: Type-2 AGN and Ellipticals & Spirals sources are concentrated at low redshifts, whereas Pure Starbursts and Type-1 AGN show a larger span. Correlations between hard/soft X-ray and ultraviolet, optical and infrared luminosities, respectively, are reported, showing a noticeable improvement when only Type-1 AGN are considered. The correlations get worse when the soft X-ray luminosities are used instead of the hard X-rays. Type-1 AGN show the highest values of hard and soft X-ray luminosities of the sample, together with the AGN contaminated by Starbursts, whilst most of the Ellipticals & Spirals show the lowest values, in agreement with the typical hard X-ray luminosities of the local population of cool ULIRGs. Pure Starbursts and Type-2 AGN present intermediate values of X-ray emission, very similar to those of warm ULIRGs. For the 20 objects with double detections the percentage of Pure Starbursts increases up to 48%. SUBMITTED TO ApJ.