There is no such thing as “full frame equivalent aperture”
A 50mm f1.8 lens will be a 50mm 1.8 lens regardless if you stick it on a 1" compact sensor, an APSC, a full frame or a large format Pentacon 6 that shoots on film. The lens is 50mm 1.8, and does not care about the sensor or film it has behind it.
(f number is a divident meaning a 50mm lens stopped down to f2 has an actual open aperture diameter of 50mm/2=25mm)
Of course, crop is different, but if you shoot the same focal length, aperture, shutter speed and iso, with same subject distance, on a full frame and a crop sensor, and you crop the FF image in post to ⅔ of the original, you will technically get the exact same photo. Same exposure, same depth of field.
The only difference you get is sensor quality, namely pixel count and density. Of course, this will mostly affect high ISO noise, you will be able to shoot at the same shutter speeds on same focal length and aperture you would be on your Fuji, but you will probably have more noise. But denoise in post processing is so good now that with a high end compact camera you will probably get very acceptable final results.
One more thing, which can affect your image quality is the quality of optical elements. It is possible that compact cameras’ glass is not as good quality as your detachable lenses on your milc, especially if you use pro grade glass.
Sidenote: the only meaning of “full frame equivalent aperture” is depth of field. It goes like
If you want the same field of view and depth of field (“bokeh”) as what you would get on a FF camera with a 100mm f2.8 lens, but on a micro four thirds body (2x crop factor), you will need a 50mm f1.4 lens. (Half the focal length, half the aperture)
You can say now that your 50mm has a “FF equivalent aperture of f2.8 on M43”, but that’s a horrendously incorrect and misleading wording of the actual settings
There is no such thing as “full frame equivalent aperture”
A 50mm f1.8 lens will be a 50mm 1.8 lens regardless if you stick it on a 1" compact sensor, an APSC, a full frame or a large format Pentacon 6 that shoots on film. The lens is 50mm 1.8, and does not care about the sensor or film it has behind it.
(f number is a divident meaning a 50mm lens stopped down to f2 has an actual open aperture diameter of 50mm/2=25mm)
Of course, crop is different, but if you shoot the same focal length, aperture, shutter speed and iso, with same subject distance, on a full frame and a crop sensor, and you crop the FF image in post to ⅔ of the original, you will technically get the exact same photo. Same exposure, same depth of field.
The only difference you get is sensor quality, namely pixel count and density. Of course, this will mostly affect high ISO noise, you will be able to shoot at the same shutter speeds on same focal length and aperture you would be on your Fuji, but you will probably have more noise. But denoise in post processing is so good now that with a high end compact camera you will probably get very acceptable final results.
One more thing, which can affect your image quality is the quality of optical elements. It is possible that compact cameras’ glass is not as good quality as your detachable lenses on your milc, especially if you use pro grade glass.
Sidenote: the only meaning of “full frame equivalent aperture” is depth of field. It goes like
If you want the same field of view and depth of field (“bokeh”) as what you would get on a FF camera with a 100mm f2.8 lens, but on a micro four thirds body (2x crop factor), you will need a 50mm f1.4 lens. (Half the focal length, half the aperture)
You can say now that your 50mm has a “FF equivalent aperture of f2.8 on M43”, but that’s a horrendously incorrect and misleading wording of the actual settings