Chrome is Google's free, open-source web browser.
Some people (myself included) think it's better than Safari. Some people think it's worse.
If Safari has gotten itself into a bad state somehow where it's crashing on you, you might as well try Chrome, I guess. You might like it better.
I don't think it syncs with iOS devices though. I guess I haven't investigated this but I'd be surprised.
If an app starts crashing on you I'd guess that something has gone wrong with it internally and I'd advise deleting it and reinstalling it. But I don't know if you can delete/reinstall Safari since it comes bundled with OS X. Sorry I can't be of more help on that front.
Chrome does sync to iOS devices as long as you are signed into the same Google account on both devices.