Theproblem that your swan has is that it lacks any variation to it's game. You know exactly what you are going to get with a swan. Large, white, surly, lot of noise, a tendancy to focus on the arm. But with your goose, well things are far less predictable.
Your average plain white goose (Farmyardus Idlus) would probably be no match for even a rookie swan with little or no experience of the ring. Your Canada goose (moosus goosus) would do well for a while, proclaim to be British whilst it was on top, then slope off back to Canada once the weather over there warmed up a bit.
But you've also got your serious heavyweight geese. Your Pink foot goose (Nortonus mincus) is a big old thing that could definately cause the swan a few issues. Big on power, up for it every night, wears you down in an attritional kind of way. Makes you lose the will to live so that you eventually give up and offer yourself up for decorative art work on match boxes.
So your choice of goose would undoubtedly influence the outcome of any serious ruck.
As for sharks and tigers - over two legs (home and away) the tiger does it every time. Just got too much in it's locker for your shark.