I would go with the 17f001dx and there are a few specific reasons why. I've had a 17" HP pavilion laptop for about 5 years now and I can tell you one thing, all HP (consumer grade) laptops batteries suck... if you want good battery life then don't go with an HP. I joke that my laptop is actually a mobile desktop with a built-in UPS. That being said, HP does shine in other areas (one of them being producing low priced laptops with decent enough quality... I mean mine's held up for 5 years now and I intend on keeping it another year or two at this point).
So I would disregard the whole battery life issue altogether. Note: the 15" one will likely have better battery life initially, not just because of the screen also because of the processor. The 17" one has a A8 in it where as the 15" just has a E1, correct me if I got that wrong about the processors, and weaker chips (the E1 is alot weaker than an A8) are better for power consumption than powerful ones typically, as long as the weak one isn't paired up with a discreet graphics card, which in this case it isn't.
Now I would go with the 17" for a few reasons other than that I believe battery life shouldn't be your deciding factor. First off, neither laptop has a discreet graphics card so therefore the one with the A8 in it (the 17" one) will have better graphics performance (not just for gaming but for anything you do with it, E1 integrated graphics aren't the best and A8 integrated graphics are pretty good). In addition to that a 17" screen is alot easy to look at than the 15" one. Now that's my personal opinion and I have only ever owned laptops with 17" screens but I do believe they are better to work with, assuming you're willing to carry the extra weight around. Additionally, the keyboard has a bit of a bezel to it on the 17" one which is nice to have. Also, the 17" one should be a bit better with regards to heat dissipation (you are buying an HP so you should know it will heat up and a larger laptop just means that much more room for the heat to escape, which is a good thing for a laptop).
Now if you're not willing to carry a heavy laptop around with you places then maybe the 15" one is a better option. The 15" one also has a lot more options with regards to bags that it will fit in. The only concern I have with the 15" one is the lack of power (I'm really not sure how the E1's integrated graphics will hold up). If you're only watching videos, looking at photos, and doing basic productivity stuff (surfing the internet, using Word, stuff like that) the 15" one but over time you may find it slows down alot quicker than the 17" one just because of the processor in each.
as for the bluetooth thing, nope it is not a requirement but it does open a few doors with regards to being able to buy bluetooth mice (but those really aren't necessary)... most wireless mice (assuming they are not a bluetooth mouse) will come with a usb dongle that will act as the receiver so you don't need to worry about having bluetooth in the laptop.
hope this helps with your decision
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