It's the resolution of the image. Higher resolution = clearer picture.

720p =1280x720 resolution displayed in progressive scan

1080i = 1080x960 interlacing

1080p = 1080x1920 in progressive scan

Progressive Scan means that every vertical line is refreshed 60 times a second

Interlaced means that every other line is refreshed alternately 30 times a second.

A TV outputting 1080i will have the clarity of 1080p, but with some slight ghosting or fuzzyness.

However, a 1080i player has the same end result as a 1080p player on a 1080p tv, as any 1080p tv with a quality scaler (key word being "quality", as not all tvs are equal) will simply deinterlace a 1080i image.

Basically, a 1080i machine is really all you need, though I'd personally recommend a 1080p player if you have a 1080p tv, and since you said money is no object...

Also, remember that both formats are having a deal where you get 5 free movies with the purchase of a player.  Free movies is always a good thing. :D 

@makingmusic476:

You won't necessarily have any ghosting or fuzziness from a 1080i signal. Any non-CRT HDTV automatically displays a progressive image, and will re-format the signal to the display's native resolution, whether that be 1024x768, 1366x768, 1920x1080, etc.

Ah, I did not know that.  Then what's the point of a 720p/1080i tv?  Wouldn't it just dowscale the image to 720p?

@makingmusic476:

The specs are really just to indicate what kind of signal the television can accept and process. All non-CRT HDTVs have a native resolution at which all signals will be displayed; however, the difference in quality may lie in how well the internal scalers and such can process the information. Many 42" plasma TVs, for example, have a native resolution of 1024x768, although they apparently have some sort of additional sub-pixel processing jargon. In essence, it seems that the greater the native resolution of the input signal, the higher potential for image quality (though this means little when dealing with upscaled images). Though, as mentioned, 1080i movie input will be of no less quality than 1080p when used with a 1080p display.

Actually, plasmas have a resolution of 1366x768. 1024x768 = 4:3 and would not be widescreen. :P

But yeah, I understand what you're saying.

@makingmusic476:

Pixels don't have to be standard, they can be 16x9. Trust me, many 42" plasmas are 1024x768.

http://www2.panasonic.com/consumer-electronics/shop/Televisions/Plasma-HDTVs/model.TH-42PX75U_11002_7000000000000005702

Widescreen pixels? That's insane, lol.

Well, the pixel itself wouldn't have a 16:9 ratio, but the pixels are rectangular rather than square.

EDIT: From the specs of that TV I posted, the pixel pitch is 4:3. Therefore, you have 4:3 pixels x 4:3 resolution = 16:9.

The only reason why I'm bringing up the new feature set from Blu-Ray is because any advantage HD-DVD has over Blu-Ray is diminishing.

There are only two advantages to HD-DVD, one is price, and the other is exclusivity of certain movie studios. Blu-Ray has exclusivity of different movie studios, so it really depends on what you want, but in terms of storage, features, streaming rate, sales, overall movie quality (video+sound), Blu-Ray is either the same or better.

Actually, the programming knowledge and amount of code required for BD-java is significantly more complex than with HDi, which may prove to be a deterrent for studios deciding to develop truly interactive content on Blu-ray. A number of Blu-ray titles have already created problems with advanced features on various players. Also, Blu-ray players are not required to have an ethernet port, while HD-DVD players must have one. Therefore, the HD-DVD standard is actually more future-proof than Blu-ray in terms of ease of updating.

Again though, it's way to early to call it either way. In the long run, I think HD-DVD ultimately has the greater potential for benefit to the consumer in terms of costing, features, manufacturability, etc. Whether this potential will have the opportunity to be realized remains to be seen.