I have recently changed my approach to this and am no longer switching between iPhones. Read my more recent blog post here for details.
A while back I wrote and article on GeekDad.com about how I switch between my work provided iPhone during the work week and my personal iPhone during the weekends. It works really well for me. Then my Apple Watch arrived. I knew this was going to throw a wrinkle into how I managed my two iPhones. So far I have founds some benefits and some drawbacks...
The Pairing and Unpairing Process
First I want to explain how pairing a single Apple Watch with multiple iPhones works. You should already know how to pair your Apple Watch to your iPhone. All of the settings of that pairing are saved locally on your iPhone. It is essentially a backup of your Apple Watch data much like you would backup your iPhone physically to a computer. The only difference between backing up the Apple Watch and backing up the iPhone is that as of right now there is no iCloud backup option for the Apple Watch. This makes it even that much more important that you are backing up your iPhone somewhere. Now if you lose or damage your iPhone you will lose all your iPhone data AND your Apple Watch data. Please backup. When you are ready to switch the pairing of your Apple Watch from one iPhone to the other you must first unpair the Apple Watch from the first iPhone. To do this go into the Apple Watch app on your iPhone and under the "Apple Watch" menu option there is an option to "Unpair Apple Watch". This will essentially restore your Apple Watch to factory settings and totally unpair or disconnect it from you phone. Don't worry, all of your settings and nearly all of your data (more on this later) are still saved on your iPhone. When you choose to re-pair the Apple Watch to this iPhone again later you will start right where you left off.
Now that you have pristine Apple Watch that needs an iPhone to pair to you are ready to pair the watch with your other iPhone. Open the Apple Watch on your other iPhone and pair the watch with this other iPhone just like you initially did with your first iPhone. You will be asked to enter your "Apple ID" just like you did the first time. This is interesting, because for me my "what the app is calling my Apple ID" was already pre-populated but it was with my iCloud account and not my main iTunes Apple ID I use for App, Music and Movie purchases. Since the watch is paired to my iPhone which is signed in with my iTunes Store Apple ID I guess that is enough to give it permission to run purchased iOS apps. It looks like Apple is letting you add the Apple Watch to your list of authorized iOS devices (which is currently limited to 10) without taking away from those 10 devices. So at least for now it appears that you can run iOS apps on 10 iOS devices plus as many Apple Watches as you own.
Once you are thru with the initial pairing of your Apple Watch to your other iPhone you will notice that you are essentially starting from scratch. You once again get to choose what apps to install on the watch and how to setup your notifications and glances. There may be a way to transfer your backup your Apple Watch data from your 1st iPhone to your 2nd iPhone, but I haven't tried to do this. I imagine it would involve some kind of a hack and I'm not interested. So far the benefits of having 2 different Apple Watch configurations are outnumbering the downfalls.
Pairing the Apple Watch with 2 different iPhones has some unexpected benefits. First off, I am able to setup different watch faces and different notification settings during the work week as compared to the weekend.
Different Watch Faces:
For the workweek I am using the "Modular" watch face because it offers the most visible complication option for displaying my next calendar event/events right on the watch face. This is a really convenient feature for me as I am often running from one meeting to the next while at work and the meeting rooms are always changing. Now I don't have to pull my watch out of my pocket and fish for my next calendar appointment. This also gives me quick access to conference dial in information. Normally I would have to balance the iPhone in one hand while dialing into the conference and inputting the meeting ID and not its right on my wrist.
Different Notification Settings:
I really like this unexpected benefit of juggling two different sets of Apple Watch settings. First off, I am able to set different "Do Not Disturb times". During the work week I am up much earlier in the morning and go to bed pretty early. On the weekends I am up later and sleep in a bit, so I am able to set different times that fit my schedule. I wish Apple would add the ability to customize "Do Not Disturb" for weekday and weekends, but now I get to do that with my switching of iPhones on the weekends. I also like being able to setup notifications differently during the weekend. For example, I don't want to be notified that someone @mentioned my on Twitter while I'm in a meeting at work, but I like being able instantly respond on the weekends. Now I can set it up that way. I can also customize the notification sound volume on the watch. During the weekdays I still allow the watch to play audible alerts, but I have the volume turned way down. On the weekend I turn up the volume. Glances are also nice to be able to customize differently during the weekend vs the weekday. Glances are only handy if you limit them to just a few key apps, otherwise you have to swipe too many times to get to the glance you want.
There are two major drawbacks to pairing the Apple Watch between 2 different iPhones. First off, you don't have continuity of your health data. Your workout history is not carried over so you can't get badges like the 7 workout days in a row badge and the weekly workout summary notification isn't going to show you all of your completed workouts for the week (just the ones you completed in the last 7 days with the iPhone you are currently paired to).
However, the real drawback to the 1 Apple Watch/2 iPhone setup is Apple Pay. Apple Pay setup on the Apple Watch is separate from your iPhone. If you think about how Apple Pay works this makes sense. Your temporary credit card number is stored on each of your Apple Pay devices on a separate chip called the "Secure Enclave" and no app (other than Apple Pay) or entity (not even Apple) has access to the data stored on the secure enclave. Since you are able to use Apple Pay with your Apple Watch even if you don't have your iPhone with you, it makes sense that the watch must be independently setup with Apple Pay. So when I switch my Apple Watch from one iPhone to the other I have to start over with Apple Pay and setup any cards I want available for Apple Pay use on the watch all over again. The good news is that the setup itself only takes a few seconds.
The verification step is another story. Once of my credit cards allows me to verify with a code they email me. No problem, just a quick switch to the mail app and a copy and paste and I'm done. The silly part is that the bank mails me a physical letter via USPS every time I setup a card with Apple Pay. So twice a week I have been getting letters in the mail from my bank welcoming me to Apple Pay. My main bank requires me to call to verify. That takes a bit more time, but at least I won't be killing any trees. The good news is that once you setup Apple Pay on your iPhone it stays setup. So I am only adding my main credit card to Apple Pay on my Apple Watch and not all of my Apple Pay ready credit cards. So I only have to add one card on Friday evening and then re-add the same card to the watch again on Monday morning when I arrive at work. This is not going to change because of how the Apple Pay security is designed to work. A small price to pay in order for me to continue to only have to carry one iPhone at a time.