I happily watch pro women's soccer every week on TV. (4pm Eastern every Saturday on PAX - nice plug, eh?) Yes, there's an elite pro women's soccer league in the US, currently in it's 3rd season: W*USA
There's also a top level men's pro league, and the level of play in both leagues is high.

I also happily watch women's tennis, plus a lot of men's soccer and men's tennis.

Of course women can't compete with men in sports, like cycling, that require strength and power. They can, and do, compete with women. Women's sports are every bit as interesting as men's sports. Whether there's a market for women's sports is the question. Women don't seem as interested in watching sports as men are, and men don't seem too interested in watching women's sports...but that may be changing.