Hi,
The Satellite TV service I use uses the internet to connect to their On Demand servers.
I have two set top boxes that are capable of streaming HD content.
I have three Macs, there are 4 iPhone and 3 iPads in the house.
I have three Computers that are On (even though I am mainly using the iMac and reading the news on the MacBook Pro.
My son also has a Macbook Pro.
On top of that there is an X Box one that is sometime playing games and two TV that are also capable of Internet streaming (and are connected).
Whilst I don't think I have a lot of use my son's gaming or TV usage or my wife's TV catch ups can effect what is going on without me realising.
I know it defeats what the app and the Handoff is supposed to do but does the text also appear slow on the iPhone ? (when you are typing on the Mac)
Is it slow in the other direction, either to show in the iPhone or on the Mac.
If both are slow it is more likely to be something about the network.
If one is slow it is going to be about the app on that device.
However other than suggesting that you Turn it Off and reset it I don't have anything else as I can't test it myself.
10:14 pm Sunday; November 1, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad