Let me guess: the source image you placed in the INDD has less than 300 dpi? So when exporting to 300dpi, Indesign has to upscale, which turns out to be this way. Seems like you can't change anything here.
I tried this with an A4 page where one 300dpi photo is placed, exporting the page to a 300dpi PNG and JPEG and I can't see any difference between both images and the quality of both is very good, of course depending on the quality of the source image.
The solution would be to place a source images with higher resolution. In case there is none, upscaling in Photoshop before placing it should have better results when exporting from Indesign.