I've used both and have around 700 channels from multiple sources with overlap of channels, so is vaguely similar to your setup.
Since digital TV, I don't think MythTV has needed as much resources, but its scheduler is a relatively big hit. I've read people run it on a Pi, but presumably they don't have many recording rules (I have a couple of hundred) or channels. It runs fine on my old hardware and takes significantly less memory than my tvh (around 1/3) since information is stored in the database not in memory. Move DB on to a cheap ssd and it is fine.
MythTV has the best scheduler of any DVR. It can resolve conflicts, schedule programs to record later to ensure it can record another 'one time showing' programme, allow any programme to prefer any tuner (so prefer higher quality satellite for movie and low quality aerial for news; re-record an SD programme if it is later shown in HD), etc. But the Kodi integration has always felt poor and would occasionally hang. Retuning (scanning for new channels) is tedious if running headless due to only being X11.
I've recorded maybe eight-or-so programmes at the same time with it. You're unlikely to hit any limitation nowadays since disks are so fast and it's just a straight bit copy.
TVH has good failover of tuners, so sometimes one of my tuners will fail to tune (despite being available), and tvh will use another tuner instead. It's tuning of new channels is relatively easy. The dev version has artwork, which I find useful, and a number of filters such as by season and by year, which helps when you only want to record 'S9 or later of X' or 'all 4* movies made after 1990'.
I've recorded 30-or-so programmes at the same time (by mistake) from attached tuners.
Its Kodi integration is good since one of the developers of the plugin pushes through Kodi interface changes too in order to get new features in.
Tvheadend also has good sat>ip support and seems to have better tablet integration.
Tvheadend's problem (with few tuners) is that its scheduler is basic. Even with numerous tuners, I've had a number of occasions where programmes have been missed, which never happened with MythTV.
The limitation with Pi (from what I understand) is that its network and all USB ports share the same bus, so you are limited by how much you can record (especially if using a NAS instead of a usb drive). So, USB2 is 480mb/s but say your stream is 20mb/s (from network), 20mb/s (write to disk); then if you're streaming it would be read from disk 20mb/s and 20mb/s write to client. So, you'd probably be limited to around 5 client (40mb/s + 40mb/s = 80mb/s; 480/80=6, but assume lose some through general overhead). So, not the biggest of limitations, but something you could hit in holiday seasons.
