I cannot comment on the HTC phone or the various unique things UK since I'm in the US. What I can say is that I was in a slightly similar boat as you on a few things. My PC is on it's way out (sporadically works then doesn't) and I was on the fence as whether to get a new PC, a tablet or the Note 3. I was using a Motorola Razr Maxx HD, which I liked.
In the end, after much consideration I decided to give the Note 3 a go and I have found it to be a wonderful productive device that does pretty much everything I need it to do. I rarely turn on my PC anymore and genuinely feel I don't need a tablet either. This phone does everything I need. I do email, social media, banking, work documents, photos, videos, music. I have yet to find something it cannot do.
If I lost it or it was stolen, I would run right out and buy another one at full off-contract price. It's that good. I came from the iPhone a couple phones back and the wife uses an iPad, but these Note 3's are the bomb. Do you have the ability to 'test drive' one for a couple weeks in the UK like we can in the US? If so, you should definitely give it a try. You won't be disappointed. And if you are, you can always return it and go the tablet route.