There are two issues here: what do advisors want, and what can they observe? In principle, I think most would choose Person 1 over Person 2, if they knew all the facts. However, this choice will not typically arise in practice, because they won't be able to verify the "thirst for knowledge and good grasping power".
Classroom performance, no matter how excellent, is generally not sufficient for admission to a strong graduate school. The problem is that lots of students get excellent grades, and these grades are only loosely correlated with research ability. The only way to stand out is to do something that's fundamentally more impressive than doing well in courses; this could be a research project, or a substantial exposition, or coding, or any number of other things. Research has some advantages, since that's what you're aiming to do in grad school, but it's by no means necessary. However, if you don't do any research, then you'd better have some other way of demonstrating your talent.
For example, if Person 1 has done no research, but wrote a beautiful, 80-page undergraduate thesis giving an exposition of forcing and the continuum hypothesis, then that might count for more than most undergraduate research projects. On the other hand, if Person 1 can point to nothing concrete except course grades, then that will likely be a problem.