How to quickly drain iPhone's charge to compare batteries
Geekbench

I don't have Geekbench 4, but according to this Primate Labs support page (1 Feb 2017):


  We're hoping to re-release a battery test for iOS in the future but as of right now we don't have an exact timeline of when that will be available.


So you would need to double-check with them prior to download whether the battery test has been re-released yet (although based on the screenshots I think not).

In terms of the test itself, I do have Geekbench 3 installed on my iPhone and it includes a Run Battery Benchmark function.  

This is a very lengthy battery test designed to totally discharge a fully charged battery (the app prompts you to plug it in and charge it to 100% before testing). That said, it is actually possible to run the test with only a partially charged battery. 

The app also keeps a history of the benchmarks - so it'd be easy for you to keep a separate record of which battery was installed at the time of the benchmark.

My assumption is that when it is re-released, the same functions would be included.

coconutBattery

In case you haven't heard of coconutBattery, this is an awesome app that you can install on your Mac (if you have one). You can then connect your iPhone to your Mac and this app will show you the battery's current charge, its full charge capacity, and its design capacity (among other things). It also keeps a history, so it'd be easy for you to keep a separate record of which battery was installed at the time you connected your iPhone to your Mac.

If you have a MacBook of some sort it'll give you a whole heap of info relating to your MacBook battery too.

Other iOS Battery apps

There are countless iOS battery apps available, most of which I think aren't worth the download. 

However, Battery Life is one of the best (make sure it's the one by Robert Tkotzyk - as there have been a couple of copies that essentially look exactly the same). I have found this app's Run Times to be more accurate than many others. By Run Times I mean it provides an estimate of the remaining runtime for various functions (e.g. talk time, browsing, video, etc).

Do your own 'real life' testing

Doing some real life testing provides the advantage of determining the exact battery life for your exact scenario (iPhone model, battery, installed apps, etc).

For one possible way you could do this, refer to my answer here. As you can see, it's quite involved if you want to ensure accuracy, and it will take some time.

Summary

My recommendation would be to contact Primate Labs to seek the current status of again including a battery benchmark test on their iOS app. I think this will do exactly what you want without all the mucking around.

Beyond that, I would try coconutBattery out (it's free to download) and give Battery Life a go too. 

NOTE: - I have no affiliation whatsoever with any of the products described in this answer.