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I thought the same when I sold my iPhone 5 and bought a Nexus 5 (I know it's only 5"). I thought I would use my iPad Mini less, but no.

I'm selling my Nexus to buy the new iPhone - having now tried Android, I'm not a fan. However, because I'm used to having a larger phone, I think I'll go for the 5.5 iPhone, and I can't see it replacing my iPad.
The Nexus 5 is the same size as the 4.7" iPhone 6. I sold my Nexus 5 for an HTC M8, which I thought was too big at first and considered down-sizing to a 4.7" iPhone 6. But the 6 would be a downgrade in terms of resolution and battery life, so now I'm thinking of getting the 5.5". The 5" M8 actually isn't too bad, so maybe I could et used to the 5.5" 6+.
 
What's easier to lug around? An iPad Mini (fits in a coat pocket, purse, small bag) or a Mac computer (briefcase)? What's quicker to access at any time (i.e. boot time, program loading time)?
a 11 inch Macbook Air is almost as portable as an iPad Air..it's far from being a briefcase..boot time is also super fast thanks to SSD,agree not always on like iPad but still pretty fast.
Also if you add that keyboard to the iPad then carrying a 11 inch MBA might be even easier.
For those who do use the iPad to write (how exactly is writing on a Mac better than an iPad with a Bluetooth keyboard? I've timed myself and it's the same speed, same efficiency), you're not going to get the size with an iPhone, and you're not going to get the same portability with a Mac.
Typing on a (11 inch) MBA with real physical keys beats typing on touch screen any day.there is no question about that..
if you add a keyboard then there is an extra item to remember to take,extra item to carry and then there is possible need to re-sync the kb etc,whereas with a small 11 Inch MBA you have it all in one,ready and it's capable of much more..

Photoediting? That's debatable and depends on what you use to edit and the amount of editing necessary. Most photos I take require very little editing, so a program like Lightroom is perfect and runs perfectly on the iPad Mini.
Again it's definitely much more convenient to edit on a real laptop (say a 11 inch MBA) with track pad vs editing via touching the glass on an iPad..specially with iPad mini..not saying it's a poor experience with iPad as I so some light photo editing with my iPad Air but it can never beat accuracy and convenience of a real Mac.
How about things like shopping and checking things off a list? I use my iPad Mini all the time for grocery and other shopping. iPhone is too small for this, and there's no way I'm lugging around a laptop to do it.
I agree shopping and web browsing is usually more convenient on an iPad vs a laptop or current iPhones,however I was referring to a 5.5" iPhone..which should provide a very similar experience to an iPad mini..

I'm not saying iPad is suddenly obsolete,I'm saying for someone who owns a Macbook Air and an iPhone 6 Plus,there is very little reason (if any) to own an iPad Mini.
 
The Nexus 5 is the same size as the 4.7" iPhone 6. I sold my Nexus 5 for an HTC M8, which I thought was too big at first and considered down-sizing to a 4.7" iPhone 6. But the 6 would be a downgrade in terms of resolution and battery life, so now I'm thinking of getting the 5.5". The 5" M8 actually isn't too bad, so maybe I could et used to the 5.5" 6+.

"Downgrade" in resolution is more of a downgrade in spec numbers on a spec sheet than anything visually apparent during actual use. Can't comment on battery life since it varies by usage, brightness level, etc.

You'll also be getting an upgrade in overall build quality, fit, finish, polish, no carrier logos stamped all over the place, no waiting around for Android Kit Kat Nestle Crunch update to be available for your device once a carrier approves it, resale value, and cohesive ecosystem compared to a fragmented world of HTC, Google, software skins, and general yuckiness.
 
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