Observation: people who love their iPhone and/or Apple products tend to spend most of their time thinking about how much they love their Apple products. There is high mix of complete apathy and indifference when it comes to competing products, especially android.
I do find that at least on the two forums that I frequent, Macrumors and Androidforums, there are a lot more iPhone users gushing about their phone than Android users. On G+, there are quite often Android users who post screen shots of their home screens that they customise. I guess this is the equivalent of gushing about their phones.
Many people who love android spend an inordinate amount of time thinking about Apple, how their new toy compares to Apple, and why Apple lovers don't love their new android toy as much as they do.
I do this this on Macrumors and on G+. I don't see a lot of this on Androidforums. For me personally, I own an Android phone, but I do have family members who use iPhones who are not as proficient in tech devices in general as I. I end up being the tech support person for my extended family and end up having to fix issues and teach them how to do certain things.
My iOS experience is a little skewed since I have to deal with things that don't "just work" on iOS. The same things tend to "just work" on Android most of the time. The latest issue is sending a picture via WhatsApp. On Android, I go into my gallery and open the picture. Then I tap on the share icon and select WhatsApp. That doesn't work on iOS. On iOS you have to go into WhatsApp and then from there compose the message and then tap on the icon to include a photo. You can also on Android compose the message first and then attach the photo. It is things like this that make me feel iOS is more limited when compared to Android. There are other things about iOS that frustrate me as well.
The other half of the time android lovers toil with trying to make their phone work right. A lot of time is spent "fixing" over "doing". The fixing part creates delusions of grandeur where installing a Rom and rooting makes one the next Bill Gates, while an Apple lover would have been done already and moved on to next thing.
I find that there are very few Android users who do advanced things like custom ROMs. Most Android users I know just use their phones as is and add apps or widgets to add capabilities. It's like most iPhone users install apps.
A lot of the customising I do is organising my apps and widgets so that the most commonly used apps are in my centre home screen. Less used apps and widgets are on the other home screens. Apps that I don't use or rarely use, I don't even put them on my home screen. If I do need them, I just go into the app list and launch them from there.
I consider this type of organising akin to organising apps into folders and moving apps around on iOS. I do use folders myself on Android. On iOS, I would likely also organise the most often used apps on my first home screen and in the middle. I would likely use folders as well to make it easy for me to find the apps I have.
Android does allow for more flexibility in organising the various apps and functions. I do use an alternate launcher. I use it to remove the app dock you see on the bottom of the home screen. I also configure each home screen with 6 rows (instead of 4 + dock) to make more efficient use of screen real estate. I wouldn't consider this "fixing" my phone. It's an option I have on Android and I'm just exercising it. An alternate launcher is just another app I can install on my phone that gives me flexibility in organising my apps.
Over time, phone users install more and more apps on their phone. When I do that, I may need to do some reorganising, particularly if I am using a new widget that takes some significant space on my home screens. On iOS, if you install an app you use very often, you may reorganise your home screen to either move it to the first home screen or to the dock on the bottom of the screen. The place where iOS puts the icon by default may not necessarily be the ideal place for it. On Android, you would do the same to put the app icon where it makes the most sense. That process may or may not involve reorganising things. Also, over time, the apps you use most often may change and may require reorganising as well.
If you don't care about organising your apps, you can just leave the icons where the OS puts it. You can do nothing more than this both on iOS and on Android. If you use very few apps, you may not need to do very much organising of apps or even not at all regardless of whether you use iOS or Android.
There are phone users of both operating systems that like to do a greater level of customising than what is available out of the box or what is inherently intended by the OS or phone manufactures. There are iOS users who jailbreak their phone to allow them to do more. There are also Android users who like to root their phone and install custom ROMs. This level of customisation is beyond my expertise. I think that a small percentage of users of both OS's do advanced things with their phone like this.
The amount of time you spend "fixing" things just depends on how fussy you are or what exactly you are looking for. For instance, there are a variety of weather apps available on Android and iOS. They all offer different features and looks. Whichever one you like the most depends on what features you want. I personally want to see radar imagery showing precipitation in my area. This feature is better on some weather apps than others and is not available on all weather apps that I have tried. I had to try different weather apps to find the one (or ones) that I like the most. I would think that you would have to do that on any OS if you are picky about the apps that you use.