iPhone 5 to 6 Plus here. I don't think the average person would notice the speed improvements THAT much. Sure, it's faster, but for most people it doesn't need to be this fast. iOS 8 feels a bit snappier, but I've still noticed it lagging a few times. Probably just needs a software update. I find myself using my iPhone to browse the web more because it's much easier to read and view images on.
The biggest difference is obviously the display and it is gorgeous. The extra crispness is a little bit noticeable if you hold your phone close, but most people won't notice that. But they will notice the colors, contrast, etc of the screen. It's not overpowered either. Just seems very accurate (I'm a graphic designer, so take that opinion as you wish). It's really neat to be able to have extra information on the screen. It truly feels like an iPad Nano.
The second biggest difference to me is the camera. It really is an improvement, and it's crazy how fast it focuses now. The faster HDR is a really nice feature because you now get shots without the sky or something being blown out, but you can also take the shots very quickly. The panoramas are smoother and easier to take than on my 5 because the optical image stabilizer. On my 5, if I deviated off course by a small amount it would put black chunks at the top or it would end up "smearing", for lack of a better word, the image as it stitched it together. In my tests with the 6 Plus, it can capture the frames so quickly and smooth out the motion so well that this doesn't really happen very often, if at all as far as I could tell. Slow-mo is really fun to play with, but time will tell if this feature is something I would use very often. Lastly the camera flash is leaps and bounds beyond the iPhone 5. My wife still has the 5, and the difference between shots using the flash is astounding. Everything is so yellow/green. The white balance is worth it, and the power is really strong. I could take photos of completely dark rooms in my housecompletely darkand on first glance you wouldn't even notice the light wasn't on in the room. They still look slightly off because of the way shadows work, so it flattens the image somewhat, but still rather impressive.
Lastly, the final big difference is the battery. After a full day of work yesterday (first full day since I got the phone), the thing was at 90% when I got home at 5:12. Usually my iPhone 5 was between 40-50%. I only use my phone a moderate amount during the day: Checking email, iMessages, browsing the web a little, maybe a quick game while I'm waiting for someone to show up to a meeting, etc. In the evening I use it a lot more, and even more so since it's a new device to play with. I used it probably 3/4 of the time from 5 until 11:30 when I finally went to bed. That's about 5 more hours of use streaming videos, playing with the camera, browsing the web, chatting with people, emailing clients. The thing was at about 40% when I plugged it in for the night. I forgot to check usage before going to bed, but my usage during the day at work was about an hour and a half with 9 hours of standby. I usually keep the brightness at about 40%, with bluetooth and location services turned on. My iPhone 5 was the same, but the brightness was a little lower, around 30%. I might increase the brightness on my 6 Plus up to 50%. I know, cray cray.
Final thoughts: Don't get it if you have small hands and need to sometimes use it one-handed. Just reaching across the screen in portrait with your thumb can be a chore. I'm talking about side-to-side, not top-to-bottom. For reference, my hands are slightly above average. I also highly recommend a case as the device itself is quite slippery. I used it without a case for the weekend, and then my Apple red leather case came yesterday morning. It's expensive, but the grip is fantastic while still sliding smoothly into my pocket. Speaking of pockets, don't get this phone if you have skinny jeans and intend on pocketing it. I don't wear skinny jeans and it fits comfortably, but it is somewhat more noticeable than my 5especially in certain pairs of pants that are a little more snugand by no means tightyou can see the outline of the device fairly well.
Hope this helps! You can always order one and if you don't like it, take it back for the other. I did this but ended up liking it, and I've been extremely skeptical of larger phones for years. I'll admit it, I've been changed. But I do feel like Apple has done the best job out of any company making a larger phone. The fact that it's a little narrower helps, I just wish it was even slightly more narrow, and a little less bezel on top and bottom. I don't find myself using reachability too often, but it is very handy when I do need it.
