Never heard any complaints from the people I know with Verizon S4s. I know 3 people. They don't complain, and have nothing but good things to say about their phones. The one that I see (and often use, several times a week) doesn't perform badly, doesn't lag, doesn't stutter. I think these issues are blown way out of proportion and is a hold-over from years-old issues with other Samsung devices (If you didn't use an OG Galaxy S, and many with the newer phones didn't, you don't know what lag looks like, Lol).
As for the G3. No, I wouldn't recommend it.
The in-use battery life has been widely reviewed to be inferior to other devices. I"m sure someone can link some sensationalist benchmark to try to disprove, but that's like one out of about 20 and the one I know most will run to doesn't really give any info as to their methodology and the scripts they use to run the tests. Every other review ranks this device even below the iPhone 5S in-use for battery life, and phones like the Note 3, M8, and S5 beat it easily.
In performance benchmarks it also scores terribly compared to other flagships, and why? Because of that screen. The phone uses a ton of muscle to drive those pixels, and that means the device heats up quickly and can more easily overheat than other devices. As a result of that, LG get the battery life they do not from the B.S. about graphite in the battery, but from thermally limiting the performance of the device. That means, your 2.3GHz G3 is going to be running at like 800Mhz most of the time, and when it comes time to play games or even navigate around the UI the phone is prone to heating up which kicks in the thermal limiters resulting in a performance drop, stutters, and lags.
That QHD screen is ahead of its time, and the other design decisions they made (like decreasing the bezels to create a 5.5" device that is smaller than competing 5" devices like the M8") means:
1. They couldn't put an appreciably bigger battery in the phone, and
2. The device is simply not as efficient as those others in dissipating heat, because all the components are closer to each other.
It's Summer. If you're going to go to the beach on a 90 degree day and snap photos, this phone is going to have an issue with it.
The only thing about this phone that is an improvement which doesn't come with a serious drawback is the laser auto-focus, and that's been matched by software in other device so it isn't really a big selling point (the OIS+ may be, though, if compared to devices without it - especially for 4K video but that's going to make your device heat up fairly quickly and that's a much bigger concern with the G3 than something like the Note 3 at this point).
