No, not mean the DVR server,...what mean is you are comparing 2 different client apps that are on on different hardware, software, network stacks, and functions.
You only stated a brief, not really insightful specific use case with no further insight.
U can send in diag info to Channels form the slow device and they can see if there is something they can recommend to u.
What version of the AppleTV app are you using, the stable or the new Beta?
What is the make/model of your Android device?
Have u tired both on a wired connection to eliminate the wifi radio hardware difference factor?
I get what u are suggesting, but based on what little info you posted, we can only guess at your setup and knowledge level.
I do not have an Apple TV, or iphone, but on my Pixel 3, over remote wifi, or LTE, it connects to my home server in just a couple secs. (I have 500meg up/down dedicated fiber at home) and my remote wifi location is 100 megs down and my LTE signal is strong with about 90megs down.)