I'd favour the Nexus 7
I'm going to echo what seems to be the consensus in the replies so far.
The Playbook is a really nice piece of kit, solid construction, nice velvety finish on the back so that it never feels like it's going to slip out of your hand, very nice screen, good sound, and the UI is very nice to use.
That's the plus side. App support is somewhat wanting. My main bugbears are no Skype (and it looks like no possibility of it coming), a lack of anything to connect to a media server (I point it at a web server I've installed on my NAS), and an inability to play video with anything other than AAC audio.
I can't say about the iPlayer, 4oD etc as I've never tried.
Android apps can be sideloaded as has been pointed out, but there are some restrictions on what will work (camera access is out for one thing). Another problem I've found is that the sideloaded Greader app I use to read blog posts is a bit unstable and when it goes down, the only way to recover involves rebooting the tablet, which is a lengthy process.
There are a few other little niggly issues as well, but you'll get that with any device.
Now, having said all that, I got mine for free via a RIM developer program last year, so I can't complain about being hard done by, Despite what looks like a list of woes, I like it a lot as a simple convenient net access device (I used it almost exclusively while in France for 3 weeks last year). If I had to part with my cash however, I'd go the Nexus route, and I don't think I'd recommend it for your mum with regard to the issues above.