As someone who purchased amps based on an itch (and they were from Emotiva...and I will never buy from them again), my recommendation is to go with the HTPC unless you are noticing some audio issues at your listening levels. When I bought my amps, my mid-level Pioneer actually did have problems playing dynamics at higher volumes, but my newer and higher-powered receivers have no issues. That, and my original Pioneer sounded just great at my normal listening levels. Like I said, I also had the itch.
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That 5308 has a good bit of power, and the E400 and S900 models that I own that have less power can drive my speakers to reference levels with eye-watering dynamics. I honestly doubt that you'll hear any difference at all if you add an amp. Having all of your movies readily available, though...now, that's handy.
On a related note, I use an older Mac Mini as a HTPC with Kodi and it works fantastically well. Incredibly small and essentially silent.