I've no experience of the S8 beyond playing with them in shops. I've been using the Pixel 2 (smaller model) for a week. I'd note that the S8 is different in different countries: the North American moydel used a Qualcomm processor and a Sony camera sensor, the rest use a Samsung processor and sensor.
Battery life: all I can say is that I've found the Pixel 2 very good. Battery life really is individual: it depends on how you use the phone, what your coverage is like, how high you set the brightness, etc, so one person's experience is likely to differ from another's. But I've consistently got a full day's use with 7 hours screen on time with what I find a comfortable brightness, so I have no problems with it.
I don't know how to answer your second question, because it is too vague. What actually do you want it to do?
I don't like over-processed photos, so in that respect the Pixel is better as a camera for my tastes than the S8. But many people like Samsung's processing. I can only suggest you look at reviews, samples, and user's photos posted on the web, and decide for yourself which one you prefer (if either).
What sort of storage issues do you have in mind? The S8 has 64GB + SD expansion. The Pixel has no expansion, but has 64GB and 128GB options and comes with unlimited Google cloud storage for photos and videos. It really depends on your requirements.
Otherwise, what else matters to you? The Pixel has better speakers, the S8 possibly a more attractive design. The curved sides of the S8 are either a plus or minus to you, depending on your tastes. The S8 has more features, but it depends whether you need them. The Pixel unquestionably has better software support, and longer (3 years of OS updates - which is a plus if you keep your phones that long, irrelevant if you don't). And they are quite different in their interfaces: the Pixel is pretty much stock Android, while Samsung are as far as you can get from that while still having Android underneath. Or you may not care either way: both are perfectly usable. The S8 has a headphone jack, which is more convenient than an adapter but I couldn't say how the quality compares (I do slightly prefer the HTC adapter to the Google one on my Pixel - both are compatible so I have the choice). The Samsung display is brighter and more exaggerated in its colours: again, some like that, some don't.
I'll end with the advice I always give with these things: go into a shop and handle both, and see which you like best. Both will work well, so simply which you feel happier with is an important consideration, and only you can judge whether one simply feels better to you than the other.
(Of course the literal answer to the question 'which would you choose?' is that I chose the Pixel, even though I could have got the S8 much more cheaply. But the right choice for me - and I do feel this was the right choice for me - is not necessarily the right choice for you).
