[Verizon Samsung Galaxy S 4] nickhimself:
Okay, so there have been a few of us who've been experiencing really terrible 4G download speeds, most notably so in the Play Store. I'm talking Kilobytes per second here, people. I could transcribe the code and compile it faster than this stuff is downloading.

Anyway, I believe I may have fixed the issue. I've rebooted a couple of times and my changes have persisted through, so I'm hopeful. My download speed went from being measured in KB to MB which made me feel like my phone wasn't trying to operate on dial-up with some free hours left over from one of the thousands of AOL free trials discs found laying about in the early 90's.

So, here's what I tried BEFORE my fix:

-- Various 3G/4G Speed/Network/Signal Optimizer/Fix/Strengthen/Repair apps on the Play Store. Two of those apps actually helped my download speeds for the first app I downloaded from the store; after that the speeds went right back to being dismal and embarrassing. Nothing else helped at all.

-- *#*#4636#*#* to Phone Information and toggled various network preferences. Nothing affected my download speeds.

-- Tried various Mobile Network options in the Settings menu. Nothing helped.

-- Toggled variations of Roaming modes, network types, etc.

-- Flashed back to stock.

-- Flashed to Slim Bean (what I was running before)

-- Tried dirty flashing over the roms after getting everything set up

-- Cleared Dalvik, Cache, Fixed Permissions

-- Completely wiped my entire phone and started from fresh

-- Tried custom kernels

-- Went to the Verizon store and got a brand new sim card

-- In Build.prop I changed ril.subscription.types from NV,RUIM to RUIM,NV. Some google search led me to a forum where someone suggested that. It didn't do anything for me.

-- In Build.prop I saw ro.product.locale.region was set to GB. Changed that to US and rebooted. No change.

Nothing I was doing was working. I was still getting the worst download speeds I've ever seen in my entire life. I swear to god I was getting better download speeds when I was like, 10 years old browsing the internet on a 14.4 modem on a 386 processor with Windows 3.11. I wanted to punch the internet in its e-face with my digital fist.

So, that's when I had a revelation. I just came from having a Razr Maxx that I'd flashed god knows how many different roms and kernels on over the course of the year that I'd owned it. I never had download issues with that, and it too was running on 4G LTE with a micro sim card in it. If that worked fine, then why doesn't this? With that question in mind, I remembered some of the settings I'd seen in the build.props over the past months and one of them stuck out as I was browsing the build.prop for my new SGS4:

ro.telephony.default_network

On this phone, it was set to 8, however I was 100% certain my Razr Maxx has that value as 14. I figured "screw it, let's give this a shot," and changed that value to 14 instead of 8.

When I rebooted my phone stuck at the Samsung boot logo. I had to pull the battery. I booted into recovery and decided to try something different than my usual "Welp this didn't work time to format everything and try again," approach. I wiped Cache, Dalvik, and Fixed Permissions then rebooted. The phone booted up like normal. I ran Speedtest to see if my speeds were still garbage or not. That test wasn't amazing by any stretch of the word. It was something like 6 mbps down, 6 mbps up. I was getting similar speeds before, so I wasn't hopeful. Then, I went to the Play Store "just to see," and downloaded a past purchase.

It started at 50kb and my heart immediately sank. Then, it went to 2 megs. 3.5. 6.2. 9. Download complete. I was hesitant to accept any actual change, so I downloaded another app. Same increased speed. I was happy, but reluctant. I rebooted, completely certain that my old speeds would return and I'd go back to contemplating a full factory wipe and attempt to return the device for another claiming it was defective. After the phone rebooted and obtained its data connection I went back to the store and downloaded another app. FAST SPEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEED!

I don't know what the heck changing that 8 to 14 did or what that value actually represents, but my speeds have remained "fixed". Granted, they're slower than they probably could be, but my Play Store downloads have gone back to acceptable rates so I figured sharing that information with you guys here might help at least one other person who can't understand for the life of them why their new phone refuses to go as fast as it should.

TL;DR: Went to Build.prop and changed ro.telephony.default_network to 14 instead of 8 and my Play Store download speeds went from kbps back to mbps.