Cable company DVR boxes suck. Period. They're slow, have horrible interfaces, and you usually get jerked around on the rental fees. That all being said, it has one huge advantage over an HTPC: it's easy and cheaper in the short term.
A good HTPC will blow away anything else, no doubt, but how much do you value your time and money? A decent HTPC with a Ceton tuner is going to run you $500 minimum, more depending on what you decide you really want in it - things like small case size, quiet cooling, bluray playback, etc, all add to the build cost.
And while people like to say building HTPCs is simple, it's really not. If you enjoy tweaking and troubleshooting (which a lot of people do), then awesome! But just assume you'll be spending a lot of upfront time and at least an hour a week on the thing.