Re: 808 in the Moto X Style? I heard is stutters in the LG G4.
The 808 is an excellent SoC and any lag or stutter you see on any phone that is powered by one is caused by the software running it. My wife has a G4 and, to be honest, yes, at certain times there might be a few burps or hiccups, but I really only notice them since I myself have a Nexus 6, which is smooth as silk. The 808 is pretty much as powerful as the 805 in my Nexus 6 (and Note 4 for that matter). It's fine.
Every since the Snapdragon 800 launched, phones are plenty fast. At this point, any phone that has some stutters, well, it's the OEM that wrote the kernel and optimized the graphics. That's why early software versions of the 801-powered G3 were a little rough.. .it was the first time LG ventured into QHD land, so it took a bit to optimize the graphics drivers, kernel, etc. Later versions, especially those built on the international base (for some reason, the US versions were always junk), they were pretty fluid and ran well.
On most devices, 'lag' is often just a matter of the OEM coding an extremely conservative governor and that lag you see is a bit of delay in the phone cranking up the processor speed. They sacrificed overall performance to reduce power consumption. You don't want these things running a full throttle all the time.
I am quite confident that the 808-powered Moto Pure is going to be a very smooth and nice-running device. Motorola spends a lot of effort making sure that their system modifications don't get in the way of the phone doing its thing. Everyone always would say that they optimized the Moto X to run better than it should... No... they optimized their software to NOT screw it up.