The short answer:

Bokeh doesn't increase linearly with focal length.

The longer version

_{by the way, I haven't tested my claims yet, so take it with a bag of salt}

I made this illustration to show how FF behaves to APS-C(or any other smaller sensor).
The lens makes one big round image. The FF sensor captures that rectangle in the center, because that's how a FF sensor looks like - it's a rectangle.

If we use the same lens on a crop sensor, that lens would still produce the same image, but the crop sensor will only capture the middle part, because it's a smaller sensor.

Here's where it gets a little confusing for many.
Let's say we used a 50mm FF lens. Because the APS-C sensor has a 1,5 times shorter edges(and 2,25 time less surface area) as the FF sensor, we use a crop factor of 1,5. A shot taken with a 50mm lens on a aps-c body looks like a 75mm.

While the Field of View looks like a 75mm, the picture itself looks like a 50mm cropped 1,5 times. What's the difference?

It's in the bokeh - depth of field.

If we used a 75mm lens on a FF body, we would get the same field of view, but the out of focus areas would be more blurry.

The conclusion is simply the following:

First, if we use a lens on APS-C, we'll get an image that's cropped in 1,5 times. Meaning that we get an image that has bigger bokeh(because we zoom into that picture), but a narrower field of view(50mm x 1,5=75mm).

Secondly, if we want to keep the field of view the same for both systems, we will get more bokeh on the FF sensor, because a longer lens produces bigger bokeh than what the 1,5x crop factor can make up for. That's why it's said that f/2.8 on aps-c looks like f/4 on FF.

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I thought it's good to share my thoughts on the matter, because for a long time, I didn't understand why the bokeh looked better on FF. It all comes down to the fact that bokeh doesn't increase linearly with focal length. A 75mm lens on a FF is not the same as a 50mm on aps-c.
You can think about it this way: if you take a wide angle shot at 2,8 and crop it to a very narrow focal length equivalent, the image will have a lot more depth of field than something shot with a long lens.

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My gear:

Camera: Pentax K-50
Lenses: DA*50-135 / DA-L 18-55 WR / Cosinon 1.8 50mm / Tamron 17-50
Flash: Yongnuo YN660
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