I generally play on my ipad as the graphics and game play really suits me better and I play bracket tournaments mostly. I do enjoy them but can't help miss the direct competition with another player. So occasionally I play a match or skins on the PC. However there are no live tournaments on the PC either.
I remember in 1999 the first Tiger Woods game let us play live tournaments online (and that was the dial up age) against other opponents, even alternate shot tournaments. those were announced and started at a specific time and all players needed to be present in a "tournament lobby" to join the tournament.
I would think in 2016, that should not be impossible to replicate? It was a great game mode and the games were usually 3 or 5 hole tournaments to keep the pace of the tournament flowing.
I do like the bracket format but it's a bit of a "lonely" game mode and competing directly head to head would be way more fun in my opinion ...