I used to think this was going on too until I realized it was the cable I was using in the car vs home. At home I had a 6 foot cable and in the car a 3 foot. The 3ft was able to deliver a full 1 amp, but the 6 was limited to 2/3 of n amp due to it being low gauge wire. It was a cheap cable (about $1 when I bought 20 in bulk.)
As a result I was able to quick charge in the car but at home I never reached quick charge.
The phone limits to 1 amp draw. There is nothing special about it. No matter if you use a 10watt, 12watt, or 40watt, the phone is always going to self limit to 1 amp
Also note that a phone will only draw 1 amp and quick charge when the battery is below 80%. Above 80% there is a drop off to about .8 amps and reduces almost linear to 100% (about .4 at 90%)
I've done way way way too much testing with over 21 USB adapter/chargers and about 16 different brands/types of cables. Assuming the charger is iphone/iPad compatible it will always get identical performance on any iPhone. Depending on if you have a good or cheap cable, it could reduce that limit of current draw.
Stick with apple certified cables. if you're paying less than about $11 (depending on length) for a lightning cable, it's it's highly unlikely it's certified or decent quality.
All of my testing and investigation began because I found an inconsistency in charge performance and wanted to test it with real meters.
I have switched to using almost exclusively the Anker 40W 5-port charger
http://www.ianker.com/support-c7-g345.html (they have a new 60W 6-port). For cables I'm using Monoprice or AmazonBasics.
For the car I'm using a TechNGo (sold at Walgreens) 2-port charger which delivers at least 3.2 amps. It charges two iPhones (1 amp each) at max rate. Their cables are also fine, but not too cheap. Still they are OK to get in a pinch. I've tested a bunch of car chargers and they all work well since little electronics is necessary because it's already DC current unlike a wall charger. So pretty much all, even 2 port, will deliver at least 1 amp per port unless they say otherwise.
Anyway, people will believe what they want but I'm 100% sure based on my extensive testing that an iPhone will never pull more than 1 amp for charging and all chargers that perform at 5 watts or more and a decent cable all perform identically.
Now when it comes to iPad, it's a different story. You're best off with a good high watt charger and you definitely need an Apple or certified cable to get over 2 amps (12 watts.) That's one reason I just use the Anker. It's versatile, 5 ports, and feeds anything as much as it needs.
An Apple 12W is $20 and I got several Ankers for $25 on sale, and they're 5 port. So I went with the value there.