Ainz Ooal Gown and Arc are both MMORPG players who managed to get transported into the world that they formerly played in. This trope is commonly referred to as an isekai and serves as one of the biggest similarities between Overlord and Skeleton Knight in Another World.
The most conspicuous similarity between the two shows is the fact that both protagonists are transformed into skeletons. Where Ainz and Arc differ, however, are their respective classes, their preferred forms of combat, and how they roleplay.
Although Ainz is a skeleton, his class in the game is magic-oriented; thus making him more of a combination between an evolved lich and a skeleton mage. As such, Ainz is able to utilize a wide variety of long-range and large AOE attacks, making him the most dangerous character in his respective world. This is not to say that Ainz does not use melee, however, as he frequently does so while disguised as his alias "Momonga." Arguably the largest difference between the two stems from how Ainz roleplays. Since Ainz's character was created for PvP combat, he puts a lot of effort into maintaining his character's persona as an indifferent and powerful villain. Considering how nice Ainz actually is, this tends to lead to many funny hijinks resulting from his tsundere-like personality.
An unexplored factor possibly leading to Ainz's cold roleplay is the graphic conditions his Earth is in the year 2138. In the Earth of Overlord, there are many salient parallels between the real world and Earth in 2138. Like the real world, Earth of 2138 is ruled by oligarchs. The primary difference is that in 2138, the less fortunate are vividly aware of how unfair their position in life is and how powerful the wealthy truly are. The original world of Ainz was polluted beyond repair, a select few rich controlled the world's politics and economy thus mining its resources until the inevitable hunger riots took place. This greedy and grotesque world likely had a great effect on Ainz's choice of villainous roleplay. As a person normally without power, it is not inconceivable for him to want to be the one with authority for a change. This is a noticeable difference between the two series as this dark background serves to shed a great deal of light on why Ainz behaves so radically different from Arc despite being thrust into near-identical circumstances.
Arc, as the title of the series implies, is a skeleton knight and as such he is reliant on melee forms of combat. This is not to say he cannot use magic however as he was demonstrated to be able to use fireball in the initial episode, heal in the second, and his cape provides a mana regeneration effect; implying that he utilizes various magics in his arsenal. Since Arc's class is Holy Knight, he can use any ability from classes that he has upgraded from previously. Unlike Ainz, Arc does not roleplay as a villain and as such he tends to bring a jovial nature to his anime. Arc ends up contemplating much more on the positive impact he can bring to the world around him than Ainz typically considers. This is evident from the name of Skeleton Knight in Another World, Episode 1, "The Wandering Knight Sets Out to Make the World a Better Place."
This results in Arc being portrayed as the hero whereas Ainz subverts this by pretending to be a villain. The realization that Arc is not roleplaying as a villain like Ainz, forces one to realize that Overlord and Skeleton Knight are vastly different in how the main character interacts with the world around him. Another important difference to note is that Arc retains his senses of smell and taste and is required to eat, unlike Ainz. Without spoiling the answer, one should remember this difference will prove to be an important distinction in between what kinds of skeletons they are in the future. The differences between Arc and Ainz primarily boil down to how they choose to roleplay their new lives, which gives each series a fresh and interesting twist on the isekai genre without having either one become too similar to the other.
Skeleton Knight in Another World and Overlord are available for streaming on Crunchyroll