Who's older: Wolverine in vibranium shield. However, they have something else in common: they are, by far, the two oldest Marvel movie superheroes; Logan credits his long life to his mutant healing factor while Steve benefits from the Super Soldier Serum and time travel.
Although Captain America had starred in low-budget movies, Wolverine led the way into Hollywood blockbusters with 2000's Avengers films eclipsed X-Men in of box office and critical and fan acclaim.
Within the last two years, fans have watched the poignant endings of Jackman's Logan and Evans' Cap: Wolverine died a noble death in Logan while saving the universe in Avengers: Endgame. So by the time Logan and Steve Rogers' stories concluded, they were Old Man Logan and Old Man Cap. Given Logan's birth year, it should be cut and dry that he's older but Cap's time travel has really closed the gap so let's determine who is really the oldest:
According to X-Men Origins: Wolverine, James Howlett (Logan's birth name) was born in 1832 in Canada's Northwest Territories. His mutant healing factor and claws manifested in 1845 when he was aged 13, which is when he ran away from home and became a soldier, fighting in the American Civil War, both World Wars, and Vietnam. Many years later, although it's no longer clear exactly when because the Logan's alternate future of 2029. This means Old Man Logan was 197 years old when he died.
As for Captain America, Steve Rogers was born on July 4, 1918 in Brooklyn, New York. In 1943, the undersized but big-hearted patriot enlisted in the US Army and received the Super Soldier Serum, physically transforming him into a superhero dubbed Captain America. After Rogers fought in World War II, he was frozen in the arctic ice in 1945 and was revived right before ed his shield to Sam Wilson at the end of Avengers: Endgame.
So, Wolverine is older than Captain America when fans saw them last. But Logan does die in 2029; if Steve Rogers lives past 2029, he'd be 189, still younger than Logan by 8 years. But, since there's no telling when when the X-Men the MCU (and both heroes may be played by different actors when it happens) is anyone's guess.
