I see the odds of XMR overtaking BTC being close to nil. That said, I believe there's a high probability it could be a strong 2nd, overtaking LTC as BTC's "silver".
I'm certainly not going to say it will. But I will say there is a rational reason to expect that it might.
Bitcoin was supposed to be digital e-cash. Cash has to be fungible. Monero is the best fungible digital e-cash contender out there right now. The day people start to worry about whether the funds they are being paid in are tainted. They start to feel that sense of creeping dread that maybe that 20 grand they just accepted as payment for their car could be worthless. That is the day they switch to XMR in mass. Unless bitcoin manages to overcome the politics that are burdening it and find a solution to this problem. Which they might.
Right now that proposal is for a soft fork and it is essentially a hack. Consequently confidential transactions will consume far too many resources to be practical. A hard fork could solve this. But then there's that politics I mentioned. A hard fork is extremely political when it comes to bitcoin.
*edit* also what smooth said. thanks smooth.