Would it really? Look at PS3 - a year later, significant price difference and no major difference in hardware units sold.
Arguably, going head to head with Microsoft's marketing dollars could be a more significant roadblock. A few months may give Sony the time and space to properly differentiate their efforts.
PS3 also faced a major constrain that benefited 360 : due to the rise on budgets the 3rd parties needed to go multiplatform, and exclusivity deas were too expensive.
So a lot of major IPs that were in the past more related to Playstation went to 360 since day one. So people who wanted to play at launch the new big Final Fantasy, Resident Evil, Tekken ot GTA didn't need a PS3.
Most of them did the jump early in the gen. There were also some cases were some previously MS exclusives went multi but this happened mostly in the 2nd half or the gen and were mostly current gen exclusives or IPs that didn't sold a lot of millions in previous gens.
That was coming off the success of all conquering PS2. I wouldn't be willing bet their brand is as strong this time around... especially thanks to Vita.
There's nothing wrong with Vita, it's a great device but a bit expensive that like 3DS or PS3 had a weak start.
Just need more mass market appealing games (according to Metacritic had more and better games during 2012 than 3DS so quantity and quality is there), a price cut (very likely to be made as part of a console cycle), and maybe a bit of extra marketing.