Think people are interchanging the 4.7 iPhone 6 (750p screening) with the 1080p 5.5 iPhone 6 Plus and that's a mistake.
The 1gb ram is ok on the 4.7 inch 750p screen. But it's the 5.5 inch iPhone 6 Plus 1080p sceen where the 1gb made the 6 plus stutter "lag" even on Day 1 with iOS 8 Sept 2014.
So the 4.7 inch regular size iPhone 6 was ok with 1gb. Apple just thought they could get away selling the 6 plus 1080p with the same 1gb of ram.
Notice for 2016 apple put 3GB ram in the iPhone 7 plus vs 2gb ram in the regular size iPhone 7. That's to handle the better camera features in the iPhone 7 plus.
Apple knows it made a huge mistake with the iPhone 6 Plus in the ram department. They thought they could get away with it.
You raise a good point in distinguishing the 6 from the 6 Plus, and that is a fair thing to bring up in this thread for others who are in a similar position as the OP.
That said, I don't think the 6 was "ok" with 1GB of RAM....it was still a struggle to multitask with it, just like the 6 Plus or any iPad with 1GB (the Air 1 was abysmal at multitasking). Sure it was smoother than the 6 Plus, but that UI lag is more attributed to the downscaling that the 6 Plus model had to do, not so much the lack of RAM (though it is ultimately a combination)...but you can still experience lag and stuttering on the 6 Plus without any apps open.
I agree with you that the 6/6+ should have had 2GB of RAM, that was an oversight on Apple's part.
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It is worth mentioning in this forum dialogue that the 6 is still quite a capable device today, as is the 5s, on iOS 10. Both are similar in processing power and both give the user reliable performance today. Neither device has to downscale like the 6 Plus did. If someone is on a budget and cannot afford a 6s (for example you may be able to find a 6 for 2x cheaper than a 6s on say Kijiji, or a 5s 3x as cheap...big, tangible savings for some people) then the 6 and 5s are still good investments. 6 will give you better battery life and extra screen real estate, but you effectively get the same performance as you would with a 5s. That said, the 6 plus is not worth the investment I don't think.
Further, if you can afford to get a 6S or 6S Plus, then certainly make that choice over the 5s/6/6Plus. The 6s and 6s plus really improved performance...it wasn't just tossing 2GB of RAM that did it, the type of ram and it's speed was improved, the processors were significantly improved as well...something Apple did not significantly improve going from the A7 to the A8
So if anyone is in same shoes as OP, get the 6s or 6s plus if your budget can accommodate it....but if it can't, don't be afraid to go with a 5s or 6. Stay clear of the 6 Plus. Or use your current, older/other device for a while longer and wait for the 6s/6s Plus to become even more affordable.