Is there an advantage using the iPad vs. iPhone for gaming apps?

Hi,

My friend and I have been having an on-going discussion about playing games on the iPad versus the iPhone. Giving a little background as to why this question came up, we both play similar games (Crossy Road, Flappy Bird, Stack, etc) and constantly try to beat each other in the high scores department.

While he uses his iPhone exclusively, I use both my iPhone and iPad for gaming. Often times, I prefer the iPad...due to the larger screen and less strain on the eyes. When I register high scores on my iPad, he playfully states that I am cheating due to the larger screen. So this leads to my question of gameplay. Not being a technical person in regards to hardware, is the gameplay the same regardless of the device or is there an unfair advantage by using the iPad. My argument is that now with the updated Apple TV and the ability to download and play games on a much bigger TV screen, I should be getting all the high scores on there...but I am not.

Thank you in advance in helping solve this dilemma for us!