We present a large-scale study of the X-ray properties and near-IR-to-radio spectral energy distributions (SEDs) of submillimetre galaxies (SMGs) detected at 1.1 mm with the AzTEC instrument across a ∼1.2 square degree area of the sky. Combining deep 2–4 Ms Chandra data with Spitzer IRAC/MIPS and Very Large Array data within the Great Observatories Origins Deep Survey North (GOODS-N), GOODS-S and COSMOS fields, we find evidence for active galactic nucleus (AGN) activity in ∼14 per cent of 271 AzTEC SMGs, ∼28 per cent considering only the two GOODS fields. Through X-ray spectral modelling and multiwavelength SED fitting using Monte Carlo Markov chain techniques to Siebenmorgen et al. (AGN) and Efstathiou, Rowan-Robinson & Siebenmorgen (starburst) templates, we find that while star formation dominates the IR emission, with star formation rates (SFRs) ∼100–1000M⊙ yr⁻¹, the X-ray emission for most sources is almost exclusively from obscured AGNs, with column densities in excess of 10²³ cm⁻². Only for ∼6 per cent of our sources do we find an X-ray-derived SFR consistent with NIR-to-radio SED derived SFRs. Inclusion of the X-ray luminosities as a prior to the NIR-to-radio SED effectively sets the AGN luminosity and SFR, preventing significant contribution from the AGN template. Our SED modelling further shows that the AGN and starburst templates typically lack the required 1.1 mm emission necessary to match observations, arguing for an extended, cool dust component. The cross-correlation function between the full samples of X-ray sources and SMGs in these fields does not indicate a strong correlation between the two populations at large scales, suggesting that SMGs and AGNs do not necessarily trace the same underlying large-scale structure. Combined with the remaining X-ray-dim SMGs, this suggests that sub-mm-bright sources may evolve along multiple tracks, with X-ray-detected SMGs representing transitionary objects between periods of high star formation and AGN activity, while X-ray-faint SMGs represent a brief starburst phase of more normal galaxies.