Well, just because you have 4 liberties and so does he doesn't mean you should win the fight. It depends if groups can run away to get more liberties, special things at the edge/corner of the board, approach moves and so on. The way I would approach this situation is:
1) Black outside group is not going to die any time soon.
2) Black corner group is surrounded and might die.
So what happens if black helps the weaker group and takes a liberty?
$$Bc
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . 1 O . . . .
$$ | . X X X O . 2 . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$
- Click Here To Show Diagram Code
[go]$$Bc
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . 1 O . . . .
$$ | . X X X O . 2 . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$[/go]
White runs away and isn't surrounded, black fails. I also see that this corner shape is an L group and I know they are dead.
So next I try block from the other side (obviously f18 doesn't work as he can push through and capture) and read what happens if white pushes into the corner. After 3 both have 3 liberties (thanks to black making an empty triangle) but now it's whites turn! Sometimes 4 is a tesuji but black can just take libs and win:
$$Bc
$$ ------------------
$$ | . 4 6 7 8 9 . . .
$$ | . . 3 2 O 5 . . .
$$ | . X X X O 1 . . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$
- Click Here To Show Diagram Code
[go]$$Bc
$$ ------------------
$$ | . 4 6 7 8 9 . . .
$$ | . . 3 2 O 5 . . .
$$ | . X X X O 1 . . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$[/go]
But how about 4 here to take a lib? Looks like black dies if he blocks and goes straight for liberty racing (but what about 9 at b15 escape?!).
$$Bc
$$ ------------------
$$ | . 8 6 . . . . . .
$$ | 5 0 3 2 O 9 . . .
$$ | 4 X X X O 1 . . .
$$ | 7 O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$
- Click Here To Show Diagram Code
[go]$$Bc
$$ ------------------
$$ | . 8 6 . . . . . .
$$ | 5 0 3 2 O 9 . . .
$$ | 4 X X X O 1 . . .
$$ | 7 O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$[/go]
So next I read what if black takes the key point looking descent. The value of this is white taking the liberty at d19 makes his own empty triangle.
$$Bc
$$ ------------------
$$ | . 6 5 . . . . . .
$$ | 7 . 3 2 O 9 . . .
$$ | 4 X X X O 1 . . .
$$ | 8 O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$
- Click Here To Show Diagram Code
[go]$$Bc
$$ ------------------
$$ | . 6 5 . . . . . .
$$ | 7 . 3 2 O 9 . . .
$$ | 4 X X X O 1 . . .
$$ | 8 O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$[/go]
And tada! Even though after 9 both have 2 liberties and it is white to play, white can't approach black so black wins. So this would be my tentative conclusion, that black can win this way. I would then read more to check if I had missed any variations. For example as 5 was black's key point, what it white plays 4 there? He can't connect but maybe some ko? It's far more complicated than 4 = 4 => sente wins, we can see in the intermediate position it was 3 vs 3 with white sente. But 4 vs 4 with sente certainly gives us hope that it's plausible black could win.
Edit: almost forgot to say, you need to read this too, it's a bad shape for white that can run out of libs and gives black forcing moves to help the L group live, but still need to check.
$$Bc
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . O . 2 . .
$$ | . X X X O 1 . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$
- Click Here To Show Diagram Code
[go]$$Bc
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . O . 2 . .
$$ | . X X X O 1 . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$[/go]
And in this situation the outside group has enough libs you don't even need the ladder, but sometimes this can be a problem:
$$Bc
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . O 2 3 . .
$$ | . X X X O 1 4 . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$
- Click Here To Show Diagram Code
[go]$$Bc
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . O 2 3 . .
$$ | . X X X O 1 4 . .
$$ | . O O O X X . . .
$$ | . . . . O X . . .
$$ | . . . . . . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$[/go]