When Sony hit the right notes, there is no real competition.
Viable brand name throughout the world, 3rd parties wont shun them and a 1st party that consistently puts out brilliant games. Marketing deals for the biggest games, exclusive content for others and a positive word of mouth tend to go a long way.
That said, Microsoft don't need to really "compete" with Sony right now. They've already lost "the war". As long as the Xbox brand continues to be viable in the West, the Xbox will generally be a success. There will always be ports of the biggest 3rd party titles due to the Xbox brand strength in the West and by the end of this generation at least, we're gonna be seeing the Xbox One "Family" of consoles pushing 45 to 50 Million units. They need to make a profitable machine that's easy to develop for, and with Xbox Live continually bringing in money the brand itself will continue to be viable for Microsoft.
You want to know how much Microsoft currently cares about beating the PS4? They're putting 1st party titles on PC.
