"Obsolete" is much more common. If something is obsolete, no one uses it or does it anymore. "Obsolescent" is rare, and means "in the process of becoming obsolete". If something is obsolescent, people still use it or do it, but much less often than they used it in the past, and we can expect them to use it or do it even less in the future. Programs coded in Flash are obsolete. The Flash platform isn't updated anymore, and it is impossible to run Flash on modern computers. Landlines (phones that aren't cellphones) are obsolescent. They are much less common now than they used to be, and they are becoming rarer every year.