<p>It depends on how you define "better".</p>
<p>Here are two examples from my experience.</p>
<ol>
<li><p>While at Princeton I had tenured professors examining my youthful literary theory ideas as though they were valuable and pointing me toward works written in Classical Greek that they could read when I couldn't (as they knew 7 languages to my 4). It meant I got to have the experience of being a real scholar without having to become one. For the most part at state schools those kinds of professors don't spend that much time with undergrads.</p></li>
<li><p>After I took 4 years out of the workforce to have kids, my Princeton diploma got me consulting jobs just because people rightly or wrongly assumed I was smart.</p></li>
</ol>