So I was in a similar position a few years ago (that is looking for a good wide angle) and I was really keen on the 14-24 f/2.8, but I ended up going with the 16-35 f/4.
Price was not an issue – as it happened I could get them for the same price – what ultimately did it for me was the lack of available filters for the 14-24. Sure, you can get these custom filters, but I like to shoot with ND filters, so it was a big issue for me.
Secondly, I am usually shooting landscapes, often in bad terrain/weather and a big sour point for the 14-24 is that there is zero protection for the front element and in snow, it will build up on the "petals" rendering it useless (by all accounts).
Sure the f/4 is quite a bit slower, but it has VR which is pretty darn good and it is as sharp if not sharper than the 14-24. There is more distortion, so for architecture it can be somewhat annoying. I often wish for a f/2.8 when shooting starscapes and I was really sad not to have it for shooting the northern lights (take the widest thing you can get your hands on!) but overall it is a much more practical lens for me.