I can't help you much on this choice yet since I am going through the same selection process you are, but here are a few points to consider:
I believe the Denon AVR-884 and AVR-1804 are the same unit, with AVR-1804 being the U.S. model number. If you buy an AVR-884 in the U.S., most likely you will not be getting a U.S. warranty.
If you care about warranty coverage, you should check the manufacturer's web site to see whether the vendor is an authorized dealer. Denon and HK can and probably will deny coverage if you purchase from an unauthorized dealer. Some retailers may be authorized to sell products in the store but not online.
If you want to save some money off retail prices and still get a warranty, check out the authorized dealers who sell refurbished Denon and HK items. HK sells refurbished items directly to the public through its own web site and eBay.
HK is known for rating its amplifiers more conservatively than other manufacturers including Denon. In any event, I think many people place too much emphasis on power ratings. Unless you are trying to fill an enormous room or have very inefficient speakers, 50 watts per channel should be more than enough.
If playing LPs is a big factor for you, note that the Denon includes a phono input but the HK does not. You can buy a decent phono preamp from Radio Shack online for about $25 or pay more for an audiophile-quality unit.
The HK model includes an EZ-Set utility for setting relative speaker volume; Denon does not.
Denon includes remote room capability; HK does not. You would have to go up to the AVR-330 (or the discontinued AVR-325) to get this capability from HK.
HK includes pre-outs for all channels; Denon includes one for the subwoofer only (to be used with a powered subwoofer). The extra HK pre-outs are important only if you think you might want to add some kind of outboard amplification later on.
I have not heard either unit so I cannot comment directly on sound. Both manufacturers have solid reputations. Based on other comments I have read, I would expect the HK to have a sound that is a bit more palatable to audiophiles, especially in analog two-channel material. This factor is important to me since I will be using the receiver mostly to listen to classical CDs. (I can't afford to buy separate two-channel components at the moment.) But judgments about sound are subjective, and some people hear differences that others don't. In my opinion, a good component should accurately produce the sound quality of the program material and not add any coloration of its own. If you have a chance, bring a few CDs to a showroom and see how the units perform in stereo. If the music sounds right, then movies will sound right.
Personally, I am leaning toward the HK AVR-230 (or AVR-330 or AVR-325), but I still might buy the Denon AVR-1804 at the right price. I believe both manufacturers will be updating their lines in a few months, so prices for current models may go down then.
Good luck, and let us know what you end up deciding.