Skills:
Kutuzov - Salvo, Explosives, Land Fort, Plain Fighting, Cover
Scharnhorst - Salvo, Artillery Master, Plain Fighting, Inspiration
If we remove all useless skills:
Kutuzov - Salvo, Plain Fighting
Explanation - Bunkers are rarely used by the AI, so Explosives is bad. Land Fort is only for defensive fighting, which arty doesn't do well. Cover is bad, as you shouldn't leave arty in the open when there are enemies around.
Scharnhorst - Salvo, Artillery Master, Plain Fighting, Inspiration
Explanation - Artillery Master is still a useful skill in the endgame, even though crits are weak. More damage? I'll take it. Inspiration is actually good with heavy cavalry running around, and morale is always useful.
Title - Kutuzov has King while Scharnhorst has Prince. Scharnhorst will get 30 BA (for a total of 64 BA) and Kutuzov will get 23 BA for 74 BA. Scharnhorst will have +27% and Kutuzov will have +30% in all for stats. A Kutuzov win, but 3% is 2-3 damage in reality. Not much.
Cost - Kutuzov is 2030 medals in cost with 4 levels of good skills provided. Scharnhorst costs 1170 medals with 6 levels of good skills. Obvious winner is Scharnhorst.
Verdict - Scharnhorst will have 2 good skills over Kutuzov, which will make up for his 3% less damage. He also is almost half of Kutuzov's cost, for more! An obvious Scharnhorst win.