There isn't a right or wrong way to drawing fursonas. I think manga style is widely used, which is why I think you can see most furry art in that style too. I myself prefer trying to draw as realistic as possible, and someone else I know wants to draw more toony (not necessarily manga).
I think you should just draw the style you like to draw, not what is most used. I think in time people will ask you to draw stuff, because your art is different than most (most being manga that is).
So drawing in your own style is right. Drawing in a style you don't like doing or just because it's used much is 'wrong'.
I hope this answered your question