Fast Resume is something which is grossly misinterpreted by tech bloggers and windows phone community in general. Fast Resume isn't new to Windows Phone 8.1. It was present in Windows Phone 8 as well.
What Fast resume does is that it makes task switching faster. When you leave an app using back/home button, the app gets suspended in the background. You can resume it using task switcher(long pressing back button). But, traditionally, if you try to open that same suspended app through its tile on start screen/app tray, it would kill the suspended process and restarts the app.
With Fast Resume, you can resume to that suspended state from anywhere. By using task switcher or taping tile on start screen/app tray etc. It will resume app from that suspended state instead of restarting it. IT DOES NOT MAKE IT ANY FASTER.
http://msdn.microsoft.com/en-us/library/windows/apps/jj735579(v=vs.105).aspx
And btw, Skype already supports Fast Resume.
http://allaboutwindowsphone.com/flow/item/19908_Skype_gets_Cortana_integration.php
The problem with resuming screens and slow speeds in WP8.1 is probably due to the fact that Microsoft changed Memory allocation setup in WP8.1. Up until WP8, every app would be allocated a specific amount of memory irrespective of how much the app need it and in most cases the amount of memory allocated would increase the amount of memory required.
In WP8.1, the memory allocated is nearly identical to the amount the app actually requires.
What this means is that there will be more memory available, so, more apps can stay suspended in background.
So, how does it affect speed? Well, when you open an app, it needs lots of memory to render it at first. I'm guessing is that, in WP8, the apps would have excess memory allocated to them so switching between them was faster because they didn't need extra memory required for rendering. But, with WP8.1, the apps have the exact memory allocated to them and when you switch between them, it takes time to use extra memory to render it just like you open an app for first time.
http://allaboutwindowsphone.com/features/item/20073_Windows_Phone_81_appsmultitask.php
I'm no technical person btw. And my attempts at explaining these slow speeds with 8.1 should be taken with as much grain of salt as self proclaimed tech bloggers' articles about technical stuff.
Maybe, @a5cent would like to make a dedicated thread on this topic and explain to us noobs about what is actually happening here.
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