I have no experience with the mate 9 but looking at it, it seems to be an hard choice compared to the One plus 3T. The OS on the 3T is totally debloated, the modifications introduced by oxygen OS make it feel like an improved stock android experience.
Comparing both phones in terms of specs and price I think that it doesn't make much sense to buy the mate 9, unless you really love EMUI and really need to expand the 64GB on internal memory. In that case an OTG cable an external micro SD reader can do the trick for the one plus.
One again the DASH Charge on the one plus 3/3T and 5 is absolutely fantastic, best and fastest charging system on the market.
Keep in kind that the mate 9 is 130 more than the 1+3T. The 1+5 is still cheaper than the mate 9, but it has some odd quirks that need to be solved.
http://www.gsmarena.com/compare.php3?idPhone1=8416&idPhone2=8073
Bigger battery, bigger screen plus the convenience of having a microSD card slot instead of constantly needing to carry around an OTG cable and a usb stick. 6GB is nice to have but are you ever going to need or use all of it?? as for fast charge -- mate 9 can reach 90% in 60mins
Oneplus Quotes
"A day's power in half an hour" -- While at 90% on the mate 9 will give you at least 2 days or just under 2 days depending on your usage. Hell, the longest time between charges with my daily with my mate 9 ive had while at work so far is 2days|18hrs and i still had about 12% battery left.... -- Mate 9 is better in that respect.
The snapdragon 821 and its GPU is more powerful then the Kirin 960 and its GPU but the difference isnt huge by any means.
Mate 9 might be more expensive, but you get so much more for your money as well as the 5.9" screen compared to the 5.5 of the 3T -- its an absolute no brainer. the
Honor 8 Pro is like a mini Mate 9 with a smaller screen but higher resolution and 6GB of ram. everything else is exactly the same....
mate 9 also has dual rear cameras/sensors (one 20mpx and one 12mpx) compared to the single 16mpx of the 3T but mpx isnt everything.
Mate 9 is just better. f**kers at OnePlus couldn't even let you have the second sim slot as a memcard slot which is just stupid. They should have at least given you that option between the standard version and the dual sim version.
Also, to quote the OP....
I have an iPhone 6 plus first gen and I feel like kind of replacing it this year with a new phone maybe with a better and larger screen, better battery life and better storage. Price is, naturally, also important.
Mate 9 ticks all the boxes possibly apart from the price but i bought my Mate 9 new for $500(USD) but I got $30 cashback on it also so YMMMV
Instead of these two, I recommend something cheaper and equally good. Take a look at Meizu Pro6s, Huawei Honor 9, Huawei Mate 9 Porsche Design (if money isn't issue for you), Sony Xperia XZs, ZTE Nubia Z17, Xiaomi Mi6s, OnePlus 5...
Meizu Pro6s, Honor 9, Sony Xperia XZs, ZTE Nubia Z17 Xiaomi Mi 6 are either small phones with small screens (5.1-5.5") , small batteries (around 3000-3400mAh or less) and small storage capacities (with the exception of maybe one thats expandable but paired with a 5.1" or 5.2" screen......) --- None of these handsets meet the OPs criteria. they are many steps backwards rather than forwards.
@Prima.Vera -- The mate 9 or Honor 8 Pro might be more pricey but it ticks all the boxes. and the handset will only get better over time as Huawei have coded part of the OS to learn what apps you use the most and cache it so it loads up even quicker -- almost like that of an SSD or caching software on a PC -- It will only get better over time. It does come with some bloat but a lot of it can be disabled or uninstalled
I moved from a Oppo Find 7A which was made of metal and plastic to the mate 9 which is all metal and my god does the mate 9 feel every bit as premium as any other flagship device. You definitely wont be disappointed should you decide to buy this or the Honor 8 Pro
::EDIT::
Oh and the Mate 9 has an IR blaster which means you can control your TV/Hifi or Air Con with it. Its a handy feature. I certainly had fun using mine!