tl;dr: It's almost impossible to get an Android phone repaired without parting with the phone for an extended period of time. iPhone repair services are much better.
I've been a loyal Android fan, and I use a lot of Google products. My first Android phone was a Nexus S, which I still have. I gave a Galaxy Nexus to my mom whom gave it to my brother. I got a Moto-X (1st gen, 2013) which I unfortunately lost on a bus, and the thief never returned it despite my $100 offer for lost phone. I loved the Moto-X so much that I was willing to suffer the use of the Nexus S again for three more months before I bought the Moto-X (2nd gen, 2014). At that time I could have bought an iPhone 6.
I've been very happy with my Moto-X 2nd gen, until recently I dropped it to a hard tiled floor and cracked the screen. In order to have it repaired, I have to FedEx it back to Motorola repair center in El Paso, Texas. I was given two options: (1) pay $125 now, send my phone, and they send me a loaner phone; or (2) put $500 on hold on my credit card, and they send me a loaner phone right away while I ship mine to repair. I took option (1) because they offer prepaid overnight priority shipping, and two days without the phone isn't too bad.
It turned out I was wrong. I sent my phone Thursday evening. They received it Friday morning, but did not create a shipment until the following Monday. The phone wasn't actually picked up by FedEx until Tuesday, so I only got it on Wednesday, almost a week later. Meanwhile, there was no indication when they will actually fix my phone.
The good news is that the phone I got on Wednesday was my actual repaired phone. If they had shipped the loaner and not the actual phone (which is possible for certain types of damages), there would be another week-long dance of phone exchange. Motorola should arrange with FedEx to receive packages in the morning and pickup for delivery in the evening, so that a phone can be repaired and shipped back in the same day.
My coworker had much better luck with his daughter's iPhone. When his daughter cracked the screen of her iPhone, he simply brought the phone to an Apple retail store, and they repaired the screen right away.
I suspect that service problems is the achilles heel for all Android phones. Although Android phones collectively dominate the market, the landscape is so fragmented that there is no prominent phone manufacturer. Without a prominent manufacturer, you can't achieve economy of scale with good after-sales service. Basically, once you buy an Android phone, either hope it never breaks, put up with the horrible customer service, or throw it away as an e-Waste. The first option is unrealistic. The second option is masochistic. The third option is not appealing from an environmental point of view even if Android phones could be dirt cheap---but Moto-X ain't one of the cheap ones.
That's why my next phone will be an iPhone. I actually dislike iOS with a passion, but I finally realized it's really the only conscionable choice.