First off, the question of more ram vs faster ram totally depends on your personal usage patterns. Some applications love RAM, especially graphic and video editing applications ( e.g.Photoshop, After Effects, Premier, etc.) and rendering/workstation apps (e.g. maya, blender, autodesk.) Of course, these applications also all benefit from having "faster" ram too, so the question is sometimes a false dilemma ;)
Anyway, computer memory can be termpermental, so ideally, you want to use matched sets, to try and minimize the potential for errors.
Sure, mis-matched sets can work, but unless they have the exact same rated specs and XMP profiles, you'll need to manually set the timings, voltage, frequency, etc.
Also, don't forget that if you have a processor with only dual-channel memory support, then populating all 4 DIMM slots will minutely slow-down all of the memory installed in your system (unless you have a processor with ECC Registered or Fully Buffered memory) and it also makes stability and error-checking harder.
Lastly, pay attention to the CAS latency of your existing 2133Mhz ram, you might (big might here) be able to run it faster, by dropping to ~1600, but significantly lowering the timings. If your 2133Mhz is ~CAS11, and your extra 1600Mhz ~CAS8, then you would actually increase performance by dropping the 2133Mhz to 1600 and matching the CAS8 timings (if possible.) To calculate this yourself, do the following:
(1 / speed in Mhz) x CAS = time in nanoseconds to read/write/refresh the memory, so: 2133Mhz CAS11 = 5.16ns and 1600Mhz CAS8 = 5.00ns
This doesn't account for mis-matched timings though (e.g. 8-10-10, 9-11-10, 11-10-10, etc.) for that you'd need to just calculate all 3, then average them for a final value.