There is always a lot of heated debate about 'equivalence' on the photographic internet. This usually manifests itself in how to describe a smaller, m4/3 or APS-C usually, lens as compared to a 35mm / 'Full Frame' lens. In the two images above I shot from the same place using my Panasonic Lumix GX9 fitted with the 10-25mm f/1.7 zoom at 14mm 1/30th. sec. at ISO 100 and my Leica Q2 set to 28mm 1/30th. sec. at ISO 100. So what's happening?
Firstly the m4/3 image is in a 4:3 ratio as compared to the 'FF' version. Reproduced at the same size it therefore looks like it was taken slightly closer, which it's not. Secondly, the 'FF' image has a softer out of focus background (bokeh). Thirdly the two images have different colour balances. And finally the exposures are pretty much the same. So is this equivalence?
Well yes and no. There are two things that a lens aperture setting does. Firstly it allows a certain amount of light onto the sensor and secondly determines the depth of field in the image. So the two images show roughly the same for the first but are different for the second. This is simply explained by the fact that the m4/3 lens is a 14mm f/1.7 and the full frame lens is a 28mm f/1.7.
Now we each have to decide whether light gathering or depth of field is more important to us in terms of our sensor format choices. For me it's DOF, but for others that may be different. There is also the consideration as to whether we find comparisons with 35mm / 'Full Frame' sensors useful. Now to a certain extent I'm stuck with that, having used 35mm film cameras for so long I had to get my head round all sorts of different lens sizes on the various digital cameras I have used and attempting to compare them to 35mm lenses was a useful way of working out what I was getting.
For example the first serious digital camera I used was an Olympus E-10. It had a ⅔" sensor and the zoom lens was 9-36mm, f/2 maximum at the 9mm end and f/2.4 at the 36mm end. This was described as a 35-140mm f/2-f/2.4 in 35mm terms. Now I found this comparison useful and had a good idea of what I was getting. However some, including Dpreview, push this idea that a 50mm f/2 m4/3 lens is the 'equivalent' of a 100mm f/4 35mm / full frame lens. Now I believe that this muddies the water, because it only takes into account depth of field. An f/2 lens in front of any format still has the same light gathering properties so I can't see how you can make that kind of comparison.
As I stated earlier for me large fast aperture settings are all about light gathering and being able to work in low low light. So, when I do an equivalence calculation I class the m4/3 lens used above as a 14mm f/1.7, because that makes more sense to me. And I would also suggest that this whole exercise is only marginally useful.
As photographers we decide how and what to frame in our viewfinders using our instincts rather than any kind of comparative calculations. And if we use different formats then we should expect different results. For the majority of my photographic work I usually want as much depth of field as possible, which is one of the reasons I like m4/3 so much. Now I doubt I will ever get those 35mm comparisons out of my head, but I've now learnt to put them in context, i.e. that they are only approximations and I accept the format I'm using as it is and don't try and impose any conditions on it.