I know I've read about this before here but just came across a video with a player slanting his koma …
According to comment below the video, “Its Shibutani Kazuo Sensei style .it helps the ichi no itto( thick bass) sounding more bass and also helps to find the correct positions fast whole looking the fingerboard in an angle …”
I'm not sure I get the helps finding positions fast concept with a slanted koma though.
Shorter scale will give you less tension for an equivalent tuning. That means you can use a thicker string which usually results in a thicker tone as well.
Here's a good reference about the effects of scale length for guitars, but the same applies for any kind of stringed instrument: http://www.12fret.com/2011/07/11/scale-lengths/