[Verizon Samsung Galaxy S 4] Dollyllama:
Now that I've had a few days with my LG G2 I'll comment on/compare the two based on what I've experienced.

Roms:

The main reason I switched is because flashing custom roms is imperative for me. I am going to say this: Roms for the S4 (Hyperdrive) are FAR and AWAY better than the modified LG stock roms I tried for the G2. Easier to set up, more stable, better battery life. If you're like my wife and don't care about AOSP, you're fine with the roms based of Stock Samsung (like Hyperdrive) I would advise sticking with the S4.

After giving a few of the stock LG roms a try, I decided to see what was available as far as AOSP roms. I am not a crack flasher...I'm perfectly fine with CM 10.2 and don't usually go beyond some simple customization. I like AOSP...I missed it a lot. Coming from a Galaxy Nexus before the S4, I'm glad to have it back with the G2. I had read that the nightlies for CM10 were buggy with wakelock issues. These issues are fixed by installing a custom kernel. The only bug I found was that Netflix won't play back videos...that is easily fixed by downloading an older version of netflix, applying an XPosed patcher, and then upgrading netflix to the current version through the play store. Tested and working...Chromecast also. I also read that CM had random reboot issues (but dalingrin, the dev responsible for the port was unable to reproduce them at will). The only reboots I've had are after streaming Google Play Music through my car cigarette lighter FM adapter. This is an issue with the Play Music app imo because I experienced it on my Galaxy Nexus, my S4, and now my G2. It happens, but it's rare and not the fault of the rom imo. Now that I have a stable base, I'll nandroid and try some other roms just for comparison's sake and report back if people are interested.

Battery Life

I LOVED the battery life on my S4. (came from a Galaxy Nexus so it was like night and day!) I had everything tweaked as far as using Lux to manage the screen brightness, Autostart Check and Greenify to manage apps. I could easily get over 24 hours with moderate use (4-5 hours of screen on time). The G2, while having a bigger battery, also has a newer processor. The battery life on the G2 so far for me (even on AOSP) is about the same as the S4. Again, I have the same power saving features tweaked etc. As far as removable vs non-removable batteries, that may be an issue for some people, but if/when the time comes to replace the battery, I have the tools to do it. I generally never let my electronic device batteries drop below 50% before charging them. I still have my Motorola Xoom (running 4.2.2). I bought it on release day and I still get more than a full day of heavy use out of it and it still has 50% or greater charge. Like anything else, barring equipment failure or defects, if you take care of your batteries properly, they will last.

Charging

I decided to make a separate category for charging...here's why: The S4 played charged very fast and played nicely with all of my chargers. I use THIS charger/FM receiver. I have old crappy cars without bluetooth receivers in them. (heck my suv has a tape deck in it lol). I also have an Anker Charger that i use for long days sitting behind my display table when my wife and I are vendors at craft shows. The S4 charged as fast with the Anker charger as it did from AC power. On the S4, The FM receiver/charger maintained the charge with a slow increase in % while streaming google music and charges about as fast as a USB connection while not streaming. The G2 has a fast charge feature and charges really fast using it's oem included adapter, HOWEVER it charges much slower (if at all) on the two chargers I linked above. This will be an issue down the line. I'll either have to pick up a Y adapter and separate cigarette charger and/or get a newer model Anker (or similar brand) charger that supports the G2.

Screen

I'll make this short and sweet...The screen on the G2, like many pro reviews have stated, is in my opinion MUCH nicer than the S4 for accurate colors. It is also MUCH easier to see in bright conditions than the S4 screen.

Cases/Accessories

I believe the S4 is the top-selling phone of 2013. Therefore it is financially worthwhile for manufacturers to make accessories for it. This means that there is a HUGE selection of cases, screen protectors, and other accessories. I love Otterbox Defender cases and believe in the old adage that you get what you pay for. With that being said, I was able to find practically every color of the rainbow in Otterbox cases for the S4. The G2 Verizon case (a little thicker than the GSM variant) is not available from Otterbox yet. I signed up for email notification when it is, but in the meantime, I settled on a skinomi screen protector and techskin with a Ballistic brand outer shell. It is a good case and it'll get me by until the Otterbox Defender is available but I don't like that it has a pretty slippery back and the port openings are not covered like those on an Otterbox.

Overall (the TLDR version)

Unless you have an MDK phone, If you want to flash kernels, a wider selection of roms, and having the latest, greatest processor is important to you, jump ship immediately...sell your S4 and pick up an LG G2. If you like the stock rom (or are comfortable with the variations of it that are currently offered under Safestrap), then I'll give you the same advice I gave my wife and you'll be more than happy with your S4.