Final render worse than rendered preview?

Hello everyone!
I am facing a weird issue here. Using Blender 2.76, the final render will be of worse quality than the 3D view’s preview.
I attached an image that shows what I am talking about:

On the left, there is a rendered result in UV/Image Editor.
On the right, there is an area rendered that’s contained in the image on the left.
Both use 300 samples (render settings -> sampling -> samples: both rendered and preview at 300).
But the image quality on the right is much better. On the left, it looks like the sampling rate has to be much higher to increase quality.
At the same time, 300 seems to be enough for rendered 3D view?
What do you think?

Best wishes,

I just got help. The issue is solved by increasing the resolution of the render.
It looked better in preview because I am using a retina display, which uses high dpi in preview.
So for same results, the final render needs higher resolution.

ALright, this is still weird. When I render at 4*1920p and scale the result down to 1920p, it will be better than the 1920p render. Is this to be expected?
Here is an image showing some details:

Yes, it is expected. Scaling down the image you also are resampling it “offline”

I see! Thank you for your reply! So I’ll just go with higher resolution and scale it down afterwards. Just in case I want to print it at some point.