YAGNI.
Yes, it's kinda out of place here, but that's the main reason jQuery has a larger base than MooTools. All those extras MooTools brings to the table are nice, but YAGNI.
It's not about best, it's about satisficing -- finding the adequate solution to the problem at hand. jQuery is easy to use, its primary aim is DOM manipulation. Since 95% of the people picking up javascript are doing so just to manipulate the DOM, there's no point in going through the longer MooTools learning curve. MooTools simply doesn't bring anything to the table for them that jQuery doesn't deliver with less effort.
MooTools demands more from you before you use it, jQuery lets you throw something together quickly. If you start writing large, heavy-duty js apps, you might run into some of the drawbacks of that approach, but again 95% of the folks writing js don't do that, so those things don't matter to them. They use a server-side language for the heavy-lifting and javascript for the DOM.
For that matter, they may not matter to your team, either. To take you through the lists, point by point (jQuery first):
Large community of supporters -- only slightly relevant to the project. Of more relevance to the team personally, because it speaks to life after you. If misfortune strikes (please, God, no) and your firm is gone, jQuery gets them more jobs than MooTools.
Plugin Repository -- very relevant, as it helps keep from reinventing the wheel.
Integration with Microsoft's ASP.NET and VisualStudio -- very relevant if you're a .NET shop. In fact, this alone should be the reason to switch if you do .NET.
Used by Microsoft, Google and others -- who cares?
Now for the MooTools list:
Object Oriented Framework with Classic OOP emulation for JS -- irrelevant, unless the nature of your projects makes that a plus. I don't know what you're building, but for web shops, this is only rarely relevant. Most web shops don't have enough code to make this a plus.
Extended native objects -- again irrelevant for most web shops
Higher consistency between browsers for native functions support. -- Relevant
More easy code reuse -- This conflicts a little with the jQuery advantage of a large repository. A large repository by itself speaks to reusing code. I suspect you're using a narrow definition of code reuse, here, that may not be relevant. I've reused a lot of the jQuery code I've built, as well as MT code.
Used by The World Wide Web Consortium, Palm and others. -- Irrelevant. The only relevance about who else is using what is if you're wanting a job there. There's more relevance in how many shops use it than in any particular shop using it.
There is no One True Way to approach javascript coding. Get your bias out of the way, and sit down with your team and get their bias out of the way as well. Talk turkey about the specific types of projects you're undertaking (and want to undertake) and the strengths of each library as applied to those cases. (How they might handle other cases doesn't matter, because those other cases don't exist.) You should arrive at a consensus from that.
(YAGNI = You Ain't Gonna Need It, if I need to explain it.)