The LG G3 Stylus is, frankly, LG's attempt to hit Samsung below the [pricing] belt for consumers in the market for a Note 4. The G3 Stylus, though, is a hell of lot cheaper, and for good reason: it's not a very impressive device. With a 5.5" qHD display and a quad-core Snapdragon 400 paired with 1GB of RAM and 8GB of storage, the G3 Stylus panders shamelessly to a price point, down to the capacitive rubber-tipped stylus that feels supremely disposable.
Who would consider this device? Someone who really, really wants a big, cheap phone with a mediocre stylus that goes in a slot, I guess. There really doesn't strike me as much reason for this device to exist other than as a "me too, but cheaper!" reply to the Note 4. I feel bad for anyone with this phone.
The G3 S / Beat (name depends on market), with its 5" qHD display and otherwise similar specifications to the G3 Stylus, is a bit more respectable in that at least it knows what it wants to be: a cheaper, smaller version of the G3. It seems very odd to me that LG didn't call this phone the G3 Mini - either Samsung wasn't happy with the G2 Mini name stepping on its turf, or LG may be planning a legit, high-end G3 Mini at some point. We can hope, right? (I'd personally love to see a 5" G3 with a brighter, less power-hungry 1080p panel or even a P-OLED display, personally.)
The G3 S feels like a budget phone, but it's not all bad: it seems pretty quick moving around the OS, and the texture of the rear cover is, I'd say, preferable to the smooth and glossy surface on the normal G3. The G3 S is a bit like a vinyl texture, giving it more grip. The display isn't fantastic, and qHD even at 5" is going to give you noticeable jaggies, but it's not bad if you're looking at it straight-on. The G3 S is a respectable, if relatively boring, mid-range phone that does most of the software tricks of its premium relative at a much lower price.