I bought a Raspberry PI 2 and HdHomerun about a month ago. I installed OSMC. Everything runs super smooth. There has never been any lag watching anything. I also have an Nvidia Shield and an Amazon Fire. Strictly in terms of Kodi experience, I would say the Raspberry pi 2 is best, the Shield second and the Fire third. This is probably because of the software setup. Before I forget all I did, I thought I would document my experience here in case someone is considering a similar setup.
I use the Raspberry Pi 2 both as a TvHeadEnd backend and frontend. I use the hdhomerun extend as the tuner. I also use the Shield and the Fire as frontends. Recorded shows are saved in the microSD card in the RPI.
I strongly believe the hdhomerun "extend" is the right choice currently. This thing does transcoding on the fly, so you can get the perfect quality through the network. Even if you plan to connect it to the RPI over ethernet, it is convenient to have the signal pre-transcoded so that your recorded files are smaller, and also you can stream to other devices in your home. Only warning: the hdhomerun extend has a fan, and it can get mildly noisy sometimes.
I installed OSMC. I have not tried Openelec (or XBian?). I have no reason to recommend one over the other. They both seem to fulfill the same purpose. I have only tried OSMC and I am very satisfied with it. Any of these two systems run Kodi exclusively, without anything else (not even an X server). Because of that, it is logical that Kodi performance will be much better than if you run Kodi inside a full Ubuntu installation, or Android, or (god forbid) Windows.
One thing I remember wondering when I was ordering my RPI online was whether I would need to connect a keyboard. I DID NOT. You install OSMC in a microSD card from a separate computer. Then you plug that card on your RPI and the installation finishes. You control the RPI with the TV remote through CEC. There is really no advantage in having a keyboard connected to the RPI.
OSMC is downloaded here https://osmc.tv/download/ You have to download a piece of software on your computer which will copy the operating system to a microSD card. I downloaded the installer for linux, since I use Ubuntu on my laptop. The installation went without trouble. After writing into the microSD card, I wanted to read it from my computer to see what was there. I noticed that the created partition was only about 100Mb, leaving the majority of my 64Gb card empty and apparently unusable. I remember I was slightly concerned about this at the time. But it was nothing to worry about. As soon as you insert the card in the RPI and run it for the first time, the installer program will reformat the card to its full capacity.
OSMC has a section where you select from a few additional standard packages to install. TvHeadEnd is one of them. Thus, you can install it easily just with one click in your remote control.
OSMC also comes with an ssh server preinstalled. At this point your may want to ssh your RPI from another computer. The default username and password are both 'osmc'. This is important to install some extra utilities related to hdhomerun and tvheadend. I ran the following two commands (through ssh):
apt-get install hdhomerun-config
This installs the usual utilities for hdhomerun. To be honest, I am not entirely sure how necessary it is. But it doesn't hurt to have it. The second command I ran was
apt-get install xmltv-util
This installs the EPG grabbers to use with Schedules Direct (I live in the US). If you want to use a different method for EPG and you know what you are doing, maybe you will skip this last command.
The next step is to setup tvheadend. This setup is done through a web interface, using a computer in the same network as the RPI. Here I have to say it: TvHeadEnd is a nightmare to setup. I followed the following tutorial that helped me a lot: https://www.youtube.com/watch?v=2Y-E4sQSb94
Here is the important piece of information: you DO NOT NEED dvbhdhomerun. Do not install it!!! It was designed for an older version of TvHeadEnd. New versions of TvHeadEnd (and OSMC certainly has one) support HDHomerun natively without any driver. When you go to the TvHeadEnd configuration page, select DVB Inputs, and you should see two TV adapters corresponding to the two tunners that come with the hdhomerun extend.
The reason why I installed xmltv-util is so that in the Channel/EPG / EPG Grabber tab there is a selection of modules to use. From a fresh install of OSMC, that section would appear empty. I use the one that says "North America (Data Direct)", which is for Schedules Direct. You need to set up an account for Schedules Direct before. Doing this, you get the RPI to download tv listings automatically by itself.
I also bought the two proprietary codecs for RPI2, MPG2 and WVC1. I don't know how much of a difference they make because I enabled them at the beginning. I figured that for the price of $4, it was not even worth thinking about it. The file where you are supposed to enter the codes that you receive over email is /boot/config.txt