Both resolutions are 16:9, indeed. However, to scale from 1200x675 to 1920x1080, one stretched pixel should occupy an 1.6x1.6 pixel area. Since only whole pixels can be drawn, most stretched pixels will occupy a 2x2 area, while others a 2x1*. This means that the stretched version's pixels will look uneven, thus distorted.
If you want to avoid distortion, use whole numbers for scaling. For example, use 2x, 3x, 4x, etc., so your new resolution becomes 2400x1350, 3600x2025, 4800x2700. Although these are really uncommon.
* - I'm not exactly sure about these numbers, they are just illustratory. Feel free to correct me on this,