In the pre-war and post-war years, both factories were about equal in quality, though Izhevsk was the larger factory and was first to implement innovations in design between the 2 factories. We're talking infantry rifles here.
During the war years, Tula was much slower to adopt shortcuts and never made guns as crudely as Izhevsk did in the worst days of the war, so in that sense "innovation" was not for the better with respect to quality.
In the post-war years, when the SKS became the main gun to be built, Tula was the primary factory. Far fewer Izhevsk guns were made, I think in 2(?) production years only. Then Izhevsk switched entirely to AK47 manufacture.