Verizon is rumored to be dropping the HTC One within the next 2 weeks. During an online chat with a Verizon service assistant I was told it would come out August 22nd with Android 4.2.2 preinstalled because they took so long to release the damn thing (they might have used slightly different wording), while the other US carriers are still running 4.1.2. Other rumored release dates are August 29 and September 5th. When the time does come I will be selling my Nexus 4 and jumping ship. AT&T and T-Mobile only get Edge service in my town. Sprint gets 3G, but it's slow. Verizon has the whole area covered with 4G LTE.
The HTC One, Galaxy S4, and Nexus 4 are all great devices and I thought I'd ask for opinions on the pros and cons of each. All input is appreciated.
I personally want the HTC One over the GS4 because of the stereo speakers and because I prefer Sense 5 to Touchwiz. Beats Audio, while gimmicky, will be nice with Beats headphones as well.
TLDR
For me, the recommendation really is THIS simple.
You've stated that the only carrier that offers good service near you is Verizon. You've asked which phone is better for your needs; the Nexus 4 or the HTC One. You cannot get a Nexus 4 on Verizon. Therefore, get the HTC One.
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Now, you also mentioned the Galaxy S4 in the body of your post. As to how this compares with the HTC One, here are the differences;
Build Quality/Materials - Do you prefer a naked phone or a case? If naked, the HTC One wins. If in a case, it doesn't matter so much.
Display - No clear winner here. Both are 1080p. HTC's is smaller (higher PPI) and RGB (higher SPPI). In theory, the One's display should offer more clarity, but VERY few will notice a difference at that size. Samsung's display is larger, and offers better black levels and contrast, while HTC's should give slightly better outdoor light visibility, and won't have issues with burn in.
Audio - If you prefer using bluetooth/headphones, the audio differences are negligible. They have the same exact DAC with the difference being the built-in hidden equalizer (Beats) and the 2x internal amps are for the "Boomsound" speakers, which don't factor into this equation. Most audiophiles will say that Beats is more bad than good, but I'm calling them even (again, just for headphone/bluetooth usage). If external speakers matter, the One is superior. If you won't use them, they take up space (hence why the One is of similar size to the S4 despite the smaller display). Up to you if this matters.
Hardware - The guts are essentially the same. The S600 used in the S4 is clocked 200mhz higher, and uses higher speed LPDDR3 RAM (1066) verus the 800mhz LPDDR2 in the HTC One. Performance will be near identical outside of the most banal benchmarks
User Interface - If you plan to root/ROM, this may not be a big deal. Both have GPE (stock) and Cyanogenmod versions available, which essentially negates this metric. However, at their stock interfaces, I've found the HTC One to be smoother, more responsive, and less bloated. It has its quirks (can't remove Blinkfeed from Sense, dialer and app drawer leave a little to be desired), but overall feels more polished, user friendly, and less bloated when compared to Samsung's current Nature UX incarnation.
Storage - On Verizon, your choices are 32GB (One) versus 16GB + MicroSD expansion (S4). If you don't need a lot of storage, HTC's configuration is superior because it is unified and has more initially available. If you need a ton of storage, get the S4.
Battery - Most users will get 2+ solid years out of lithium ion. Some extreme users, like myself, have to replace their batteries every 9-12 months. If you are in the latter category, avoid the One. You can work around the S4's limitations. You can't work around a dead phone short of a replacement or expensive repair. And unlike Samsung/Apple, HTC doesn't specify a threshold in their warranty at which they'll replace the original battery, giving them more wiggle room to charge for the repair.
Software updates - Like the stock market, past performance does not guarantee future performance. But, we can use it to make an informed decision. So, here's how HTC and Samsung have treated their previous main line flagships.
(2010) HTC Desire vs. Samsung Galaxy S - both phones released on Android 2.1 w/Sense 1.0 and Touchwiz 2.0. The Desire was updated to 2.3 with Sense 1.0, while the Galaxy S was updated to 2.3 with Touchwiz 2.0 before getting a final value-pack that added Android 4.0 features and Touchwiz 3.0. The Desire actually had features stripped from the final update, but the US equivalents (Evo 4G/Incredible) were largely the same phone on 2.3 as they were at launch. The Galaxy S saw significant improvements in features and performance.
(2011) HTC Sensation vs. Samsung Galaxy S II - Both phones were released on Android 2.3 with Sense 2.0 and Touchwiz 3.0 (respectively). The Sensation saw an update to Android 4.0, but due to partitioning, HTC could not push a full Sense update OTA. The Sensation got Sense 3.6 OTA, while new packaged versions had Sense 4.0, creating a fragmented experience that irked early adopters. The SII got Android 4.0, then 4.1.2 with Touchwiz 4.0/Nature UX 1.0 elements. It is rumored to get a final 4.2 update. Talk about support!
(2012) HTC One X vs. Samsung Galaxy S III - Both phones launched on Android 4.0. The One X is getting 4.2 now with rumors that this is the last update. HTC hasn't announced anything. The S3 is rumored to skip 4.2 for 4.3, with Samsung previously stating that the S3 (and Note 2) would get the next major revision of Android.
Bottom line on updates is that HTC typically does one major revision followed by minor patches. Samsung goes nuts and offers a significant update cycle. So if software updates matter long term, Samsung is the safer bet.
There are more points, I'm sure, but as you can see there are very few points where there is a clear winner. It's all a series of personal preferences, so score it up based on your needs and see which wins.