The online multiplayer didn't determine what console I got first last generation (the 360 just came out first), but the fact all my friends were on XBL kept me fixing and replacing my 360 after many red rings. Finally I gave up and stayed with the PS3 (I got a slim to play Uncharted 2). It was hard at first, but I got use to it.
Fast forward this generation almost all my friends went PS4 (only one went XBox One first). So far multiplayer hasn't been that important because there are no shooters I care about (CoD is finally dead to me). That said once Destiny comes out it will be a different story.
Still I think you are weighing multiplayer too much. You should also weigh cost, value (XBL vs PS+), exclusives (you want Halo or Uncharted for example), and power. To think someone didn't play Last of Us just because they only cared about the multiplayer on XBL makes me go :no:
Smart thing to do is discuss with your friends before anyone buys a console and decide if it is that important to you. Last June I let my friends know that I planned to preorder the PS4, and what were their thoughts.
Also in 3 years or so I wonder how much difference we will see in the consoles power wise. Will coders find ways to get more out of the One to make it seem as powerful as the PS4? Or will the PS4 just pull away when teams like Naught Dog really learn to push the power. Just look at Last of Us at the end of the PS3 cycle vs 360 games.