When uploading photos to Facebook, basically two parameters will influence picture quality. One being the picture's resolution, the other being the JPEG compression factor (0-100%) used to save the image.
From what we found, Facebook will always re-compresses images (around 85%), even if they perfectly fit their specifications already. As JPEG is not a lossless compression, picture quality can be slightly degraded with each re-compression.

Easy Photo Uploader is using a default compression setting of 90%, which is a pretty good compromise between size and quality. As outlined before, a slight decrease in quality may be noticeable.

For best results, you should set Easy Photo Uploader to high resolution (see Settings -> Resizing). Your photos will now be uploaded in the maximum resolution supported by Facebook (2048px long side). If you have a fast connection, or don't care about upload time, you can set the compression factor to 100 there, which will give you the best quality possible (may be relativized by Facebook's re-compression).