Both are not trying to do that.  I suspect Sony could rid MS of the console space rather easily; It's not in their best interest to do so though because they benefit from the competition. MS conversely created Xbox to stop Playstations growth as a brand in what they percieved as a threat to the PC space.  Additionally the means to which each company are willing to go through for success is not parallel to each other.  We have little to few examples of Sony buying their success as opposed to generating it, or devaluing their brand to maintain marketshare.  On a moral level, I find it much easier to justify the purchase of a PS4 over an X1.

@ the bold - This is not a matter of your opinion on the fun factor of first party titles.  This is a matter of your opinion on 1st party IP creation.

Halo - Bought from an independent company.

Gears of War - Bought from an independent company.

Minecraft - Bought from an independent company.

Fable - Bought from an independent company. 

What major IPs are left afterward that they had a hand in creating?

Forza; There's more, I know there's more so I'm sure you'll be able to list them off.

Sony the company was the underdog, you know this from reading one of my previous posts.  By extension of that, and given the massive loss of marketshare during the 7th gen world wide, let alone in the US, you can say from looking at sales trends that they came into the 8th gen as an underdog - We had a bankrupt Sony and the massive failure that was the PS3 combined with the then recent PSN hacking.  They were absolutely an underdog who were operating on razor thin margins.