As for which party produces larger budget deficits, the evidence is pretty clear.
Since the 1960s, budget deficits and the national debt have grown under Republican administrations, and shrunk under Democratic administrations.
I don't necessarily think that the Democratic party is inherently more fiscally responsible than the Republican party. Perhaps the Republicans have been successful at convincing people they are fiscally disciplined and Democrats are fiscally irresponsible, so that it is easier for the Republicans to get away with spending like drunken sailors and harder for the Democrats. Or maybe there is some other reason. Anyway, if you think the Republican party stands for budget discipline, you are ignoring 50 years of evidence.