These are good points…
I am seriously thinking on pre-ordering one, but sadly I have no knowledge on much of the difference between both i7 processors… let alone how the battery life goes for each. It would really be nice to know actual numbers
I do recommend you to go for the i5. Thin laptop like this have difficulty with cooling i7, and as I saw the Framework does not have fancy vapor chamber but classic fan and head pipe design.
I bought a laptop of the same kind of form factor (Thinkpad) with an 11gen i7-1165G7 … If I could go back in time I will definitly pick the i5.
The i7 have more graphical units, 96 vs 80 for the i5, it’s do offer a little bit more juice in light gaming experience, but do consume so much more power (due to the extra Xe units) … it saturate the cooling system, it can’t keep up, make the CPU throttle and be less powerful than its i5 varient in long load.
I’m pretty sure it will be the same for the Framework, so I will say:
If you want better battery life (±20%), better CPU perfs, better cooling go i5.
If you want better GPU, less CPU perfs, lesser cooling go i7.
For the difference about i7-1185G7 and i7-1165G7, there is none regarding performance.
i7-1185G7 is the vPro variant, meaning its support intel remote management functionality, it’s made for entreprise and you probably do not want it in your laptop (remote backdoor 
)
i7-1185G7 also has some fancy extra security features, you probably do not need and never ear about it (as support of total memory encryption, just in case someone want to use azote liquid on your computer to try eavesdrop sensitive data from the physical memory)
The supplementary 0.1Ghz of the i7-1185G7 do not matter, in all case your CPU will never keep its max Turbo Boost for long run, and how high it will reach will depends of the laptop cooling performance.
MSRP for i7-1185G7 and i7-1165G7 are the same, but I far I’ve saw, all laptop manufacturer charge a $300+ for i7-1185G7 instead of i7-1165G7. I don’t really believe they charge it for more profit, except if there is a collision between all of them. Probably they paid it more for it, whatever the MSRP is. But who knowns…
My 2ct.