What's holding Twitter back? They've had updates recently.
Their desire for advertising revenue perhaps.
For example, if they banned any non Apple apps in the Apple App Store, there's still ~60% of the market in other stores (Google Play/Windows Store), but that still isn't allowed and is very anti-competitive.
However, the reason why Apple gets away with it while Microsoft doesn't should be obvious if you're at all familiar with Microsoft's history and current market share numbers. (Hint: MS got hit for anticompetitive behavior when they owned ~95% of the PC OS market. Apple owns maybe 15% of the world smartphone market.)
IDC released the mobile market share 2015 statistics the other day:
http://www.idc.com/getdoc.jsp?containerId=prUS40664915
Android: 81%
iOS: 15%
WinMobile: 2%