Not a single reason? Well, with all respect, you must be somewhat oblivious to the facts. Things like OS stability, OEM support, and applications (most developers flock to iOS) are just a few off the top of my head.
I don't see any advantage there on either side. Well, if you plan on having your phone for years and years, with Apple you can usually count on updates for a longer period of time. That's not in any way relevant to someone who buys multiple phones in a year.
As for stability, all the tests I've seen point to Android Kitkat being the more stable of the two, and my own experience with the iPhone tells me that it is certainly not immune to crashes of freeze ups. Anyway, the difference is too irrelevant to even speak of.
And apps, well, there are apps you can't find on android and apps you can't find on an iPhone. 99,999 % of the time you get them on either, or at least a good enough substitute.
So yeah, outside of personal preference, no reason that I can think of. Well, come to think of it, security could be one. It's not something that concerns me personally, so I didn't think of it right away.
Anyway, personal preference will be the deciding factor anyway in 99 % of the cases, so I really don't understand why you would argue over this?
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As a small business owner i can give you some GREAT reasons. Try having employees install software that has to sync across multiple devices, and have the ability to stay up to date... when you have chosen Android as a platform, and all your employees have different Android phones, and have different versions of Android on all of those Android phones, and different versions of software on each of those Android phones. I can tell you first had... it's a royal pain in the ass. Not that you will care in the slightest way.
So get them the same make and model. Problem solved. You wouldn't get them computers with different OS's and versions, why would you do it with the phones?