I have 1 TiVo w/lifetime, and 2 DTiVo boxes. The original TiVo has been online since 1999 or so, and I've had DirecTV since 1996.
I had a short stint with Comcast and their HD DVR until Verizon came into town.
I have 2 Verizon HD DVRs.
I have 1 Moxi.
I did not take the plunge into TiVo HD, primarily because of the uncertainty of how SDV might have been dealt with; though a moot point, now with Verizon FiOS.
In a word, the overall lifetime costs of TiVo HD and Moxi are about the same.
TiVo and TiVo HD have been in the stores for years; Moxi has not been at all to my knowledge. The primary reason Moxi is seeing little to no market penetration is that most people don't even know it exists. The audience here on AVS Forum, as well as the other enthusiast sites is simply too small to make a significant dent in market share.
It has taken years for TiVo to penetrate the market, and still, with its clear lead in market share, it is still a company that is struggling. For awhile, they had some significant help in developing market share when they hitched their efforts to DirecTV. Alas, that did not continue.
The winners so far are the DVR suppliers to the cable companies - Motorola, and others.
If TiVo or Moxi truly had significant partnerships with the cable companies, there might be better market visibility. I am sure that either company would welcome such a partnership. But alas, it is not to be, except for a few successes for Moxi with sister company Charter (both have Paul Allen affiliation). TiVo has some multi-year experiments getting its user interface installed on the Comcast Motorola boxes in some markets in the Northeast.
Which is better? TiVo HD or Moxi? I'll leave it to others to debate this. From my perspective, each has advantages and disadvantages. I truly want both to succeed, because competition is good for the consumer.
What I like about the Moxi is the multi-room capabilities mentioned upthread; the Verizon FiOS boxes can do this too. Even better is Moxi's internet capability, tie to Play On for Hulu and other internet video sources; and one of my favorites, ability to play videos from my DLNA-server movie libraries. Verizon is testing some software for their FiOS boxes that provide some home media video capability, in addition to its deployed music and photo sharing.
TiVo HD can be expanded up to 2TB with certain external drives from WD (not just any eSATA drive), while the Moxi can be expanded with up to 6TB or more using most any external eSATA drive - they announced compatibility with LaCie's 6TB 4big Quadra. Of course, there are many TiVo expansion alternatives for the technical savvy; this doesn't help the average consumer, though.
I like the DLNA capability of the Moxi, since I can have easy access to any of the media on my home media server - this includes file and DLNA servers I have tested from Windows Vista, Windows Home Server, OS X, and LaCie.
I would have had a TiVo HD by now, if it weren't for the original higher cost + monthly fees, and the SDV uncertainty. But that is all sorted out now and prices are much lower now, so a moot point. Yes, there have been continued software improvements, but the TiVo HD hardware is getting quite old. I am holding out for a refresh beyond just a bigger hard drive. I expect something might show up in 2010 as others have speculated, too.
That's my 2 cents.
If you can see either box first hand, make your own comparisons. You're just more likely to see a TiVo HD first hand because of its retail presence.
Finally, as others have noted, if you only care about internet and server supplied video, your xBox or PS3 are all you really need. But for cable and premium channels, near term your choices are limited to cable-company-supplied DVRs, or the TiVo HD or Moxi boxes. ONce Win7 rolls out, look for some exciting alternatives since CableLabs and Microsoft have relaxed requirements for CableCard compatible digital tuners for Win7 based PCs.
Disclosure: as for the LaCie reference, yes, I am an employee of LaCie. I have played with DVR technology for years.