For short passing games and when the ball is on he ground 3G is miles better than grass as there is no unevenness or boggy patches and the ball rolls a lot smoother. If the ball is played in the air and bounces, it always seems to bounce/react better on grass, whereas 3G cushions it and can be a bit more unpredictable. Hence, 3G is better for 5aside, grass is better for 11 aside, unless we decided to play total tikka takka football and never hoofed or played long balls.
As for the injuries - I don't know the statistics but injuries caused when people go in for 50/50s seem to be more frequent and more damaging on 3G. I remember that preseason friendly at woodley 5 or 6 years ago and I'm not sure that would have happened on grass.