This challenge is purely for the shock factor and for entertainment, if you're wanting to have the highest likelihood of capturing a rare pokemon DO NOT ATTEMPT WHAT YOU SEE IN THIS VIDEO.
Each Tier of pokeball has a base chance to catch a pokemon, this base chance varies based on the difficulty of the pokemon that you're attempting to capture. For the hardest difficulty, indicated by a dark red circle, and seen on things like Dragonite, Tyranitar, or Blissey, the capture chances are as follows
As you can see the base chance of capturing an Ultra Rare pokemon with a pokeball versus an Ultraball is half as likely. This is a pretty huge difference when you consider that a pokemon like Dragonite has a 5% chance to run ever time you successfully hit it with any type of ball.
To increase your likelihood of a capture there are many things that you can do.
Capture Medals: Capture medals increase the likelihood that you will successfully capture a pokemon of the type that you're attempting at. If you have all gold medals you increase the likelihood of a pokeball capture by 1%, with an ultraball the increase is 2%.
Curve Ball: This is a skill based increase, this is also the only way that I throw balls. There is a bonus 10 experience awarded which is why it is always important to use a curve ball if you care at all about your level. More than this though, a curve ball increases the likelihood of a capture with a pokeball by 3%, or by 6% with an ultraball!
Razzberry: This item can be fed to a pokemon to increase your chance to capture a pokemon. Once again a pokeball gains a 3% increase well the ultra gains a 6% increase.
Conclusion: The difference between using a pokeball versus a Ultraball is that you're half as likely to capture a pokemon using a pokeball. If you're using a pokeball with a pinap versus an ultra with razzberry you have roughly one third the likelihood of a capture(7% versus 20%). Although I hope you enjoy watching this video, if you actually want to capture a pokemon I highly recommend that you use your best items!