Just after XeF2 was discovered, D. F. Smith published a short communication Xenon Difluoride J. Chem. Phys. 38, 270 (1963) mentioning the electronic structure of your second drawing.
Smith conducted infrared spectroscopy of XeF2 and wrote:
Then C. A. Coulson published The nature of the bonding in xenon fluorides and related molecules J. Chem. Soc., 1964, 1442-1454, which considered the validity of four models (plus some sub-models) of XeF2 bonding.
Coulson adds more resonance structurestructures in addition to the two mentioned by Smith, including a purely ionic F- Xe2+ F- resonance structure.
For a more recent article on the topic, see The essential role of charge-shift bonding in hypervalent prototype XeF2 Nature Chemistry 5, 417–422 (2013). (official link)
Overall, ionic contributions do need to be considered.