Thank you for all your interesting comments and your kind advice.
I'll definitely switch to Android.
My experience with my Lumia is extremely bad at the moment. I unplugged my phone at 9 AM, used it only a little to text, go on Facebook and see some webpages. Then, I used Here Maps to find directions for about 15 minutes, only to see that my battery was already at 50 % at 11.30 AM! This evening, I wanted to listen to music with headphones (jack). I couldn't listen for more than 10 secs, the phone behaved as if I was constantly plugging and unplugging the headphones. I rebooted my phone several times, but still impossible to listen to music or answer a call with my headphones. Not sure if it is a software or hardware related issue, but I'm seriously thinking of reverting back to Windows Phone 8.1 for the second time...
I'm pretty sure I'll go for the Galaxy S7 Edge, but I'm keeping an open mind. Other manufacturers than Samsung are also going to release interesting devices at the MWC, so we'll see... I'm not a real fan of the edges of the S7 Edge, but I'd like a bigger screen than the standard S7, 5.5 inches seems great and I really like the design in silver. We'll know everything about the phone by the end of the week, but I'm really interested by the battery life and the low-light pictures. It doesn't feel like a major upgrade from the S6, though... The price will be high, but it seems that Samsung will offer a Gear VR reality headset with the pre-orders, which is nice.
As for the Nexus 6P, I don't like the design very much. That's clearly not the only criterion I use to make a decision, but it doesn't help... The screen didn't impress me as much as the Galaxy S6 Edge (Plus) I tried in store. It is much cheaper than the Samsung Galaxy with very good specs, but I'm still not convinced.
Can someone explain to me what is this "Vanilla Android" thing with the Nexus? If I buy a Samsung device, does that mean that I will have to wait longer to receive updates than if I had a Nexus as they somehow need to be tested and approved by Samsung?
I don't think that carriers play any role in rolling out the updates where I live, as carrier-specific locked phones are not allowed in Belgium. You can grab an unlocked phone in any store and it will work with all the carriers. So the updates must be controlled by the manufacturer only...