Think of the two clips as an introduction to snakes in movie plots. In one scene, the hero is thrown into a pit of snakes and has to react quickly or die. In the other, the snake slyly encourages you into its' embrace and before you know it, you're trapped as the snake has wrapped its length around you and is squeezing the life from you. Both scenarios end up, more or less, at the same conclusion.
While we're not talking about an individual's death here, we are talking about the death of authority. Both the Marx Brothers and Abbott & Costello end up in the same place - the destruction of our perception of this world and its rules of order.
The Marx Brothers do this by creating a sense of equals - Groucho and Chico - negotiating over employment details in an anarchic patter, quickly ending in the destruction of order (the contract) and leaving us with nothing worth anything.
Structurally, Abbott & Costello set this up by creating, as others here have pointed out, a dominant-submissive relationship. Bud Abbott, the father-figure, impatient over the child-like Costello's fears.
Someone mentioned these men are put into situations they are unaware of and they struggle to cope as reality sets in. As Lou (the child) begins to understand their situation more fully, his efforts to bring Bud into that reality meet with resistance and the ignorance of arrogance. Slowly, the child begins to teach the man. In the end, Lou's line "Does Dracula know?" announces the reversal of their roles - the upsetting of the natural order.
Voila! They have reached the same state of anarchy as the Marx Brothers, just at a slower pace. In the end, everything you know is wrong.
As to Wes Gehring's comments, I have little patience for the position I see staked out here too often. Things evolve and what was funny in 1940 is considered stale in 2017. We who love these old films love them for a variety of reasons - the artistry, the dialogue, the cinematography, music, etc. That doesn't make them better. It makes them what they are and something we appreciate/love. I have much more of an issue with films of later decades that failed to evolve in their use of slapstick techniques and come across to me as simply lazy attempts at producing humor. The pie in the face is just not funny anymore. Everything changes for a reason.
Finally, Abbott & Costello's contribution to slapstick is the firm establishment of the true straight man/ clown relationship in film. Laurel and Hardy, who these two are so often compared two, were two clowns of different temperaments. Not so here.
I know it's been months since this class ended. I didn't have time to really participate during the time the class was open, but I'm in a slower work season now. I have a hard time reading these message boards, but I thought I should since I was having a hard time answering the questions in my own mind and needed a little prodding through others' comments. Well worth the time from my perspective. Brings so much more to the experience.