I have an iPhone 6, and I've never found myself in a situation yet where I ran out of memory. It just doesn't happen.
I wish I could say the same about my old Galaxy S3. It has the same amount of memory (in theory), but I saw apps run out of memory and force quit on it all of the time. I place the blame all of the bloatware that Samsung and Verizon added to the base Android installation.
iOS doesn't run out of memory. It kicks out apps that haven't been used in a while to free up memory for new apps. However, with newer phones, especially the 6 Plus, that happens *really* frequently, to the point that at most 2-3 apps reside in memory at once. In addition, Safari is a real memory hog, keeping pages in memory takes RAM. So if you're hoping between a bunch of pages, you'll be kicking apps out of RAM. And if you have recently used a bunch of apps, you'll be reloading pages in Safari more frequently (note, back navigation stack is included in this).
1GB of RAM on the 6 Plus is criminal. Having 1GB of RAM again in the 2015 iPhone would be... :'(
Anyway, I'm not upgrading until they go 2GB. I can't imagine the 2016 version not having it, but I swore up and down that the 6/6+ would and it did not. Sigh. :\