By implication, I'm assuming you don't want to just use an app, but instead want to do some real life testing.
However, the only way to do this and ensure some degree of accuracy is to ensure:
- that you have the exact same apps running during these tests
- all apps (and iOS itself) must be the same version
- the start and end times (and therefore also duration) are identical 1
- the ambient temperature at the time was identical (in other words, you'd have to do this in the same air-conditioned environment set at the same temperature)
In a nutshell what you would do is something like the following:
- Fully charge both iPhones and disconnect them from AC power at 10pm
- At 8am play the same movie at full volume and full brightness on both iPhones
- At conclusion of the movie, take note of the battery percentage
- Play the movie again (still at full volume and brightness)
- At conclusion of the movie, take note of the battery percentage again
- Play the movie again (still at full volume and brightness)
- At conclusion of the movie, take note of the battery percentage again
- Play the movie yet again (still at full volume and brightness)
- At conclusion of the movie, take note of the battery percentage again (assuming you've still got a charge)
Now fully charge both iPhones and leave them connected to AC power until 8am the next day, at which point you disconnect from power and perform the same test (i.e. same room, same movie, same volume, same brightness, etc).
NOTE: The above test scenario is only an example case of how you could test both iPhones. The idea of the scenario I outline above is just to get across how one would conduct a test of both iPhones to ensure some validity to the results. Or, to put it another way, to ensure you're comparing Apples with Apples (yes, pun intended). Also, one of the other factors you need to consider is your actual phone usage during the test - to ensure a valid comparison you'd really have to have the phone switched off.
Regardless of the test scenario you adopt, compare the differences in your battery percentages (and also whether one phone runs longer under the same conditions) to determine whether the $10 battery is worth the trouble.
1 Actually, while the start times should be identical, the end time may not need to be (and therefore neither the duration). This way you can take note of whether one phone can endure your test scenario for longer than the other and, if so, how much longer? For example, in my scenario, can one phone play the movie a full 4 times? Can both do that? Keep going to see if one can continue to play the movie for longer and, if so, how much longer?
In a nutshell, only you can decide, based on your test results, whether it's worth changing your battery too.