Feel free to watch almost any S4 review video.
OP, either phone is phenomenal with a custom ROM that eliminates bloatware. 
If you want loud sound, a bright and crisp screen, and less out-of-the-box lag, take the HTC One.
If you want a larger screen, expandable memory & a bit bigger battery, take the Galaxy S4.
Haha...no thread on lag goes by without Dreamliner330!
I may not agree with all of your posts, but this is pretty spot-on.
Before I did anything else when I first got my S4, I rooted it and put CleanROM on it (I had run CleanROM on my previous S3 and loved it), then setup the phone and put Nova launcher on it and did everything else to get it setup the way I want. I never really got a chance to see how much "lag" there was out of the box with stock firmware and Touchwiz launcher, but I can say that with my current setup, any lag that is present is negligible if non-existent. My only point here is that if there is a significant lag problem with this phone, I believe it's probably software related...but even then many folks using the S4 with an out-of-the-box configuration claim to have no lag issues.
I think this part here sums it up pretty well:
If you want loud sound, a bright and crisp screen, and less out-of-the-box lag, take the HTC One.
If you want a larger screen, expandable memory & a bit bigger battery, take the Galaxy S4.
Good advice. Both are quality devices, both have positives and negatives. If there is only thing I prefer about the S4 it's the battery...this is definitely the first Android phone I've ever owned that I can get 2 days on a single charge, though obviously your mileage may vary.
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