Why is it said that the Italian style can't hold their own session? 
Though almost any variety of acoustic mandolin might be adequate for Irish traditional music, virtually all Irish players prefer flat-backed instruments with oval sound holes to the Italian-style bowl-back mandolins or the carved-top mandolins with f-holes favoured by bluegrass mandolinists. The former are often too soft-toned to hold their own in a session (as well as having a tendency to not stay in place on the player's lap), whilst the latter tend to sound harsh and overbearing to the traditional ear. The f-hole mandolin, however, does come into its own in a traditional session, where its brighter tone cuts through the sonic clutter of a pub. Greatly preferred for formal performance and recording are flat-topped "Irish-style" mandolins (reminiscent of the WWI-era Martin Army-Navy mandolin) and carved (arch) top mandolins with oval soundholes, such as the Gibson A-style of the 1920s.