Hi Oliver,
Both are brilliant handsets, but it of course depends on what you're looking for in a phone.
The Nokia Lumia 820 runs on Microsoft's Windows Phone 8 platform and is powered by a 1.5GHz Qualcomm processor with 1GB of RAM as support.
The 4.3-inch Super AMOLED display has additional Nokia ClearBlack technology, which offers brilliant screen colour contrast.
There is the innovatice Nokia Drive integrated into the Lumia 820, which rivals many sat nav apps currently on the market, and an 8-megapixel camera on hand for documenting your life with 1080p video recording.
The only possible downside to the Lumia 820 is the weight - which at 160g could be considered a little on the hefty side (but this is purely down to your personal preferences).
The HTX 8X also runs on the Windows Phone 8 operating system and is the perfect platform to organise your social networking life.
Using Live Tiles (as with the Lumia 820), navigation between functions and apps is much more streamlined, with information brought to your homescreen in real time.
The 8X once again has a 4.3-inch Super LCD 2 display and is powered by a 1.5GHz Qualcomm dual-core processor.
The 8-megapixel camera (and additional 2.1-megapixel front-facing camera) and 1080p video recording are perfect for capturing life's moments and as you mentioned, Beats Audio is on hand to produce high quality sound.
Weighing in at 130g, the 8X is much lighter than the Lumia 820 - but it does all depend on which phone has the features and functions you're looking for.
My advice would be to read around both to see which you prefer.
Here's a link to our HTC 8X page if you'd like some more info: http://www.dialaphone.co.uk/phone/Windows_Phone_8X_by_HTC_Yellow/
I hope this helps you with your decision.
Best wishes,
Stefanie