Both are sageuk dramas, fictionally developed but with real-life events. It has a beautiful love story between the leads with a bittersweet ending. Deok-Im and Ae-shin are both strong and independent female leads.
Both women are willing to give up love for their principles and the life they want. The Red Sleeve occurs "before" Mr. Sunshine according to the chronological order. Mr. Sunshine takes place shortly afterward the American-Spanish War, during the Japanese occupation of Joseon, and shortly before World War I.
They have a bittersweet ending, but with a beautiful romance. Each character has a well-defined personality and a male lead who is willing to support the women they love even if it meant letting them go so they can fulfill their dreams. Two people who loved each other deeply and always wished their significant other to achieve whatever they wanted even if it conflicted with theirs.

Man to Man is more lightweight than Vincenzo. Either way, the action scenes both dramas have is fire. They both show their soft side to the people they love but seem cold to others and make calculated decisions before anything happens. Until the day they mess with the woman they love, of course. That day they go berserk and make emotional decisions.
Vincenzo is darker with an anti-hero theme. I am not sure if the recommendation would live up to the expectation the other way around: from Vincenzo to Man to Man.
If you enjoyed espionage and strong male leads who don't go suddenly good-for-the-girl cliche, Vincenzo is a good follow-up.