this is a nice example.
http://photographywisdom.com/understanding-depth-of-field-for-the-beginner-photographer-1182.html
But of course in mobile the difference wont be that drastic cause the differences are tiny. Also it's not just the aperture too, the sensor, image processor, the lens, all plays a part too. But to me, most important thing in mobile is software.
If you ask me, I think 0.1 isn't going to be a huge difference on camera modules this small... but what do i know. haha. Maybe when it comes out i'll see if i have a chance to test it out.
Anyway, camera is something that is hardware dependant in a sense. A tiny camera module like on phones will always lose to a point and shoot of the same generation (don't talk about point and shoot from 10 years ago la, lol). So software optimisation, good image processing, can make up for a lot of hardware compromises. Like even on the iPhone 6 without OIS, the camera still does well with digital stabilisation and optimisation. At this point, most modern smartphone is "good enough" to replace normal point and shoot for the casual user.
totally agree with your auto mode comment. I also shoot in auto mode most of the time even though I am okay with manual mode. I only use manual mode if i have to, or if the situation allows me to use it to capture a better/unique shot.
On a phone, i think usability is important. Like on the S6 or iPhone, there is no need to change to night mode, landscape mode, portrait mode, or whatsoever. The camera automatically takes care of everything and lets you capture a good image with as little hassle as possible. LG needs to have a good auto mode too if it wants to compete in the camera race.
Having manual camera controls isn't anything new in android now that we have Lollipop's camera2 api. if they have a bad auto mode, most people are going to end up with bad looking images because not everyone is familiar with or can be bothered with manual controls. But if they have a good auto mode, everyone who uses the camera is going to end up with good looking images.