Looking at the character creation ("Recruitment") chapter, it seems keeping Nature low is always beneficial. I get access to more traits and avoid a penalty to Fighter, a skill that will probably save my life. Also, I remember from the skills chapter that having a low Nature makes it easier to learn new skills.
What are the benefits to having a higher Nature?
Uses of Nature are a bit more spread out in the book than the consolidated benefits of keeping it low that you see in character creation, but patrolmice at any value of Nature are worth playing. High-Nature patrolmice complement the strengths and weaknesses of low-Nature patrolmice.
In both the "fight" and "fight animal" types of conflict, Nature is the skill rolled for defend and maneuver (p. 115 first ed, p.113 second ed), and Nature is one of the highest numbers you can get out of character creation, if you want it. Loremouse can substitute during Fight Animal, but the highest Loremouse you can get out of character creation is 4, if you're a patrol leader from Sprucetuck where it's your special talent.
It's very effective for lower-Natured mice who didn't penalize Fighter to take the lead when attacking and feinting in combat, then pass the lead to their higher-Nature patrolmice to defend and manuever.
If you don't want to learn a new skill, you can always default to Nature to do anything (p.235 first ed, p.230 second ed). If you're doing something that seems rare, that you're not going to rack up tests = Nature to learn through Beginner's Luck, defaulting to Nature gives you better numbers to do it. (Also, since you open every skill at 2, you're going to have a while to go before using the skill will be better than defaulting to Nature unless your Nature is very low.)
And when you default to do things outside your Nature, you have a much bigger number to absorb the Tax (margin of failure) with. Because of the way taxing nature works, you effectively have a total pool equal to the triangular number with your nature as a base. A 3-Nature mouse can absorb 6 points of Tax before going to 0. For a 6-Nature mouse, this number is 21!
Maybe this won't come up too often, but Nature is the first-order tiebreak for versus tests using Will and Health, and the second-order tiebreak, after Will and Health, for versus tests of anything else (p. 91 first ed, p. 89 second ed).
You'll probably get about two persona points per session, one for accomplishing your goal or playing against your belief, and one for one of the player-voted end-of-session awards.
You can spend persona points for a few things (p. 39 first ed, p.37 second ed). You can spend them one-to-one to add up to three dice to a roll, you can spend them after a roll to reroll all failures with an appropriate Wise (second ed only, p. 272), or you can spend them before a roll to add a number of dice equal to your Nature.
With a high Nature, this is an extremely efficient means of spending persona points for extra dice, and you can really drop the hammer when it counts.