ffmpeg: pillarbox 4:3 to 16:9
Assuming both MKVs are rips of NTSC DVDs, these are the commands you need:

For 4:3 video

ffmpeg -i "input43.mkv" -vf "scale=640x480,setsar=1,pad=854:480:107:0" [etc..]


For 16:9 video

ffmpeg -i "input169.mkv" -vf "scale=854x480,setsar=1" [etc..]


(Note H.264, the codec you are likely using, needs dimensions to be even, so specifying 853 as width will lead to ffmpeg feeding 854 pixels to the encoder and then auto-setting a funky SAR.