The reason why people ask for a TiVo is because it has the name of TiVo on it. It is much more complicated to use, does a lot less than the HRxx's, is very limited, and is ancient technology.
The reason people want it is because most people loved their SD Tivos and even the HR10-250 that Directv had. They were great and just worked and the interface was super easy to use. Then the HRxx with it's proprietary software came around and was slow, the software was buggy and there were artificial limits that didn't exist on the Tivo(50 series limit anyone?). The one thing that always bugged me on the HR2minus the 24's) was simple channel changes. To this day, on my HR20, i can type in say 265 and it will still sometimes end up trying to change to channel 26, then 5 because poorly written software that decides when the timer is up, it's gonna change the channel no matter what, even tho it hasn't processed all the digits yet.
The reason people want the HR24s and up is because they have the hardware/speed to overcome the bloated, poorly written HRxx software.
As I mentioned, the problem with the new Tivo is it is behind the times. It's on the slowest platform(HR21, yet Tivo software is surprisingly spiffy on the HR21 platform) and doesn't do many of the features that the HRxxs do, with the biggest one being MRV. I suspect this is by design from Directv to keep them one step behind their own boxes.
Anyway, to each their own.