Sans Mirror  

"Equivalence" still seems to be a topic that is misunderstood. Thus, I've created another article to explain it.

We want the same exact image: 

• same field of view
• same depth of field
• same motion blur
• same level of noise
• same exposure
• same perspective

Our goal is to produce the same size prints (output) viewed at the same distance from each.

If the different sized sensors in our cameras are all essentially equal in their base technologies, then the following will get you the same image when taken from the same spot (ISO and aperture are rounded to nearest stop; focal length is rounded to the nearest common length):

• With small medium format: ISO 3200, f/8 at 1/125, 135mm lens
• With full frame: ISO 1600, f/5.6 at 1/125, 100mm lens
• With APS-C (DX) crop: ISO 800, f/4 at 1/125, 70mm lens 
• With m4/3: ISO 400, f/2.8 at 1/125, 50mm lens
• With CX (Nikon 1): ISO 200, f/2 at 1/125, 35mm lens

Note that there's a slight problem with m4/3 in this comparison due to the change in aspect ratio. I realize that the m4/3 illuminati will complain about where I put m4/3 in these comparisons, but at a 3:2 aspect ratio to match the others, we're at 0.88 stops differential, or rounded, one stop different from APS-C. For some reason, m4/3 users are seriously paranoid about losing even a third of a stop of what they perceive to be their equivalence. I'd tend to say that that's due to self esteem issues. One problem with doing any article on "equivalence" is that if we try to get down to very specific cameras and generational sensor technologies, we lose track of the bigger picture. I'm trying to explain the generalized difference here with as many variables equal as possible. I'll leave it to you to suss out the fraction of a stop here and there where there might be differences in any current camera you're considering.  

Equivalence in this context means the same photo with the exactly same visual characteristics.

Just to be clear:

• Shutter speed doesn't change in these examples because we want the same level of motion blur.
• Focal length changes because we want the same angle of view.
• Aperture changes because we want the same depth of field.
• ISO changes because we want the same level of overall noise.
• Camera position doesn't change because we want the same perspective.

Now, in reality there’s no such thing as perfect equivalence. So many tiny variables seep in that ruin the possibility of achieving the same exact thing: 

• Marked apertures may not actually be the t/stop (actual transmission of light).
• Marked focal lengths may not be the actual focal length and there might be focal length breathing as you focus to different distances.
• No two camera makers use the same interpretation of the ISO standard (the standard has multiple possibilities to it).
• Shutters can be variable within some margin of error, and fast shutter speeds can render different, particularly when you compare electronic versus mechanical shutters.
• The sensor technologies of two compared systems are often different generations or even completely different in some important way (e.g. Fujifilm X-Trans and Sigma Foveon instead of the more common Bayer filtration).

Still, the reason why we go through the equivalence exercise is to get a sense of what we might be gaining or losing in our photography from selecting a particular camera type. Not many CX (Nikon 1) lenses were capable of f/2, for example, so we might lose an ability to do something we want to (for example, if we use an f/1.4 lens on the full frame system and then try to duplicate the depth of field of that image on any of the smaller systems such as CX, we find we typically can't do it and keep the other parameters of the image the same). 

Too many people get hung up on the word equivalence in some strange fashion. Usually the example I see someone write is “my X-crop system takes just as a good a picture as a full-frame system” or some similar variation. Nobody’s saying you can’t take a good photo with a system with a smaller sensor. What they’re saying is that the different sensor sizes play to different strengths. Another common retort to equivalence articles is that people’s egos get bruised and then they start making isolated, single point claims: “ISO 3200 is perfectly clean on my <fill-in-the-blank> system." I characterize most of these claims as "near equivalence for me." See my article on near equivalence.

In a very broad generalization for 24mp cameras (e.g. same pixel count sensor that uses the same basic underlying technologies, for example, the ubiquitous Sony Semiconductor Exmors):

• The smaller the sensor, the smaller the overall system can be and the easier it is to achieve deep depth of field. Each pixel is more prone to quantum shot noise (randomness of photons).
• The larger the sensor the bigger the overall system typically is and the easier it is to isolate foreground and background from each other. Each pixel is less prone to quantum shot noise.

Note I wrote "broad generalization" and used the word “easier." I didn’t say isolating foreground from background is impossible with small sensor cameras, such as the m4/3 models. But it might require that you step back and use a longer, fast lens, for example, which changes perspective. We can’t always take “equal” photos, but we often can take “similar” ones. 

The real question you need to answer for yourself is how much are you playing out at the photographic extremes and thus need a camera with a different sensor size that is optimal for it? For most folk, that’s not often, and APS-C remains sort of a sweet spot in the middle. For some of us, it happens more often. For example, in my small studio, I can’t get fast enough lenses and move back far enough to use small sensor cameras to get the kind of depth of field isolation in portrait work I prefer. I could get a larger studio or a larger sensor camera; it’s cheaper to get the camera ;~). 

On the other hand, when I’m photographing landscapes in the backcountry during the day, other than pixel count there’s not a lot I sacrifice when I pick up my m4/3 system versus my Nikon full frame sensor system.  

At the start of this article I listed six parameters we use to create equivalence (and there's a seventh, print [or output] magnification that might come into play for some). So, a sort of shorthand guide can be created:

• Field of view: most systems with broad and deep lens sets don't have much differentiation here. I've yet to really encounter someone who would be best advised to pick a sensor size based solely upon this factor.
• Depth of field: if separating subject from background is something you do often, you should tend to pick larger sensors over small. Vice versa, if you mostly want deep depth of field you should prefer small sensors over large. You can compensate for this factor a bit by aperture, but you run out of "fast aperture" with small systems and you run into diffraction at slow apertures, as well.
• Motion blur: one of the trickier things to track, because it's mostly impacted by the next parameter. But in general, the more you're trying to eliminate motion blur on fast subjects—particularly in low light levels—the more that suggests a larger image sensor. (Don't mistake subject motion blur for camera steadiness blur. You can use image stabilization to remove the latter, but it doesn't impact the former.)
• Level of noise: this is the parameter that often gets confused by people in discussions of equivalence. Now that read and pattern noise is relatively low in our electronics, the randomness of photons becomes the key noise element in low light conditions (this wasn't true in the earlier days of digital). If you're always working in bright light, particularly at faster apertures, I don't think you should get concerned about this. Likewise, if you use only JPEG and believe that your camera maker does a good job of noise reduction without observable liabilities, I don't think you get overly concerned about sensor size. However, the more you encounter low light and use smaller apertures, particularly if you use raw and have to perform noise reduction after the fact, the more likely that larger sensor sizes are what you should seek out. 
• Exposure: this is tricky, much like motion blur is, because it is often influenced by the previous parameter. Note closely what I have to say about using slower telephoto lenses in lower light in my near equivalence article.
• Perspective: like field of view, a system with a broad and deep lens set solves this problem for you. 

Addendum: Clearly, the camera companies want you to buy the more expensive bigger sensor cameras now. You can see it in the buying statistics, too: full frame is generating the most profit for the camera companies now, and thus getting their primary emphasis. Marketing messages are going to emphasize the "advantages" of the larger sensor more and more as we move forward, because that's what most of the companies want to sell you.