What you mean “web conference”?
Asterisk is good for conference calls. If you mean using web based phones for calls - stability depends of how stable web phones you will use.
Yes bigblue button is great. i used it. they have screen sharing, video/audio conferencing, you even do not need any phone they already have embedded the phone sdk.
If you have no idea what is is, why would you think that it might even be relevant to you. Medium length answer: svn.digium.com/svn/asterisk/ (although, if you understand the latter, you probably wouldn’t have asked the question).