Which one would you get?

Both watches are very different in intent and purpose and both could perfectly be in any collection. I like the Explorer II because, well, I would like to have one, but the older 16570 reference. 

As much I would say buy both, I chose the Rolex, In my humble stupid opinion, for me I most likely wear it more as a daily than the Cartier, but as usual buy both then you’ll be double happy!! 😉

Cartier Santos. If all you need is a good white dial watch then thats got to be the prettiest one out there. And the most classic in design. Timeless, elegant, respected, versatile… I could go on.  

Two different watches. Have both, but I’d grab the EXII 8 times out of ten. The Santos is an awesome watch. It is tough to make fit right. Everyone thinks it’s a dress watch no matter how much you want to tell them it isn’t. it scratches when you look at it wrong. That said, it comes down to personal style and preference. 

These are very different watches, but I'm guessing you haven't shortlisted these for shits and giggles. So looking at your WRUW shots, looks like you have quite a bit of Omega. You have a GMT complication in you BB Pro ae well as a Seagull and a Casio.

Your Omegas are quite hefty watches (except for the AT). Is this something you gravitate towards? Some might describe the Santos Medium as 'dainty'. As an owner of one, I can see why. Not sure how this fits with your aesthetic, but I guess if you look down and think "man, I wish this had more wrist presence", then either go for the Santos Large or the EX II. 

Having said this, IMHO a Santos would open a whole new world of style options and would perhaps offer a great contrast with your current pieces.

Having bought that Polar Explorer II, I say Polar Explorer II.👍

Chose the Santos.  Both are great watches but the bare metal numbered bezel on the Explorer 2 simply does not resonate with me.  I don't like the hands and I don't like the cyclops.

I really love the Santos.  I do think it goes great with basically anything from jeans to a suit.  But YMMV.

Difficult decision, but I'd chose the Rolex Explorer II because it's a GMT, is more resistant to smudges and surface scratches, and is slightly more versatile. That said, I'd happily wear either watch as they are both classic designs from great brands.

Nuts, I accidentally voted for Rolex. Sorry, man. 

I'd say go for the Cartier. Unless your AD have a Rolex with your name on it, you'd be better off with a Cartier Santos.