The 8X is in a different class to the others, and the Note is kind of in another class at the other end of the scale.
It depends what you value most in a phone. The most capable (read: has the longest feature list) is the Note II, but it is very large, whether that would suit what you do is obviously up for debate. Personally I have big hands, so like to one-hand operate all phones, I can't manage this with a Note II, but can with an S III. I also find the stylus a bit gimmicky on a phone, it not being large enough to really write freehand particularly well on, so it's relegated to a pointing device, but Samsung makes the interface so large, that I don't have to wear my glasses to see the screen...
Samsungs also have a "unique" feel to them, not necessarily in a good way, the back covers often feeling flimsy/cheap. The internals, and the most important parts are definitely up to scratch however.
Another point is the AMOLED vs IPS screen debate. The IPS screens in the 8X and Lumia both produce excellent, accurate colours in comparison to the AMOLEDs, which are very oversaturated, and often innaccurate. The sunlight legibility is usually worse on the AMOLEDs due to the glossy screen combined with a fairly low maximum brightness. Whether this bothers you over the advantages (perfect blacks meaning fantastic contrast, the colours do "pop" giving a bit of a wow factor) again is personal preference.
For what you're after:
Decent Battery Life: It's perhaps a bit early to confirm the WP8 devices, the WP7 devices got a large boost after launch. The Lumia gets decent battery life, but it depends on your definition of decent. For me, 2 days where I'm not really using the phone besides the occasional email/text is decent, or 1 day of heavier use (1 day = from when I wake up till I go to bed, so 7:30-00:30 ish) web browsing for an hour or two, watching stuff on Youtube/video and playing music on my way to uni and back (1 1/4 hours each way). The Note also manages this with ease, being the largest battery in a current phone (besides one of the Motorolas IIRC), though this is somewhat offset by the screen. It still gets excellent benchmark-setting battery life. The 8X has suffered a bit of a battery issue, which might be improved in firmware, but one cannot be sure. The Ativ S is just too new to accurately gauge.
Good camera: None of those phones are weak, though the Nokia has the best, especially in low light without the flash. Samsung have recently had some great cameras, in the S III particularly, which is carried across to the Ativ S and Note II. The HTC is also good.
The ability to download a whole range of software to the phone: Android's open nature means that more can be done with the development tools available, but the quality often isn't quite there - functional but somehow lacking in places that I can't quite put my finger on. Windows Phone 8 sandboxes apps, which can somewhat limit the range of what can be done (the hardware interplay apps on Android can't be replicated - things like the Torque app aren't possible on WP8 yet).
Expandable memory: Samsung is your choice here, both phones including Micro SD card slots.
If I might make a suggestion. If you're looking at the 8X with any kind of seriousness, check out the Lumia 820, it's very similar, but has the AMOLED screen instead (if you prefer), as well as 4G support and expandable storage, plus Nokia's excellent camera knowledge (though not the Pureview OIS on the 920).
Edit: damn, that turned into an essay...
TL;DR: personal preference, compare in a store to see whether any grab you instantly.
For reference, I've had an S II, now an S III, and I have a Lumia 920 ready when I can get the damn thing unlocked...
but then again it is the best phone in my eyes but then again it depends what you need from a phone and then again it depends if size matters a lot to you and you can comfortable use note 2 or not!
