Dredging up stuff that's been answered I know, however I don't think it's been answered thoroughly enough. Bang presented a very black and white picture of things and frankly sh*t is situational. There is not one set of gear for any job that can be presented as the penultimate, even individual pieces are subject to being questioned depending on the situation.
That being said, rather than insulting a person's lack of experience with a job, I'll present information in a more objective manner. While it's self-evident that the Scholar's Mortarboard +1 and the Scholar's Gown +1 are the most desirable pieces of the set, which piece is absolutely the most desirable is dependent on what you do most commonly.
Unless you manaburn all of your xp, your ideal body/head combination for main healing a party is going to be AF+1 head and relic body. In this scenario the Mortarboard +1 offers little benefit except for a meager -1 enmity however, the AF+1 body offers no benefit at all unless you are forced to rest frequently, in which case an Errant Houppelande gives the same hMP. Mortarboard +1 wins by an insignificant margin.
If you DO manaburn all your xp and have enough Elemental Skill merits/gear then an INT build will benefit you the most by increasing damage and to a certain extent Magic Accuracy. Mortarboard +1 will win with that setup, however if you build for INT or MAB in all slots then you will almost definitely need the additional skill from Gown +1 to get closer to capping MACC, the fact that a Gown +1 offers a little extra INT is just gravy.
Since xp/merits are a pretty limited part of the game regardless of the job being focused on, let's shift the lens to more advanced portions of the game.
Still maintaining the reality that sch is not as potent or accurate a nuker as blm, I'll present two different styles of gearing, a skill set and an INT set.
Until the advent of relic scholar wasn't capable of reaching the mystical plateau of 320/120 Skill/INT for nuking high level monsters, and unfortunately as it's been pointed out these are the BARE MINIMUM requirements to meet and even with them you'll be nigh on useless for AU HNM's.
Taking these facts into account I'll focus quickly on a skill set and its benefits. Lowering resistance rates will offer higher average damage over time regardless of if you are a blm or sch nuking by lowering resist rates, your spike damage WILL be lower than someone with a super int build but they will be resisted far more frequently.
This can be made analogous to a melee who focuses on accuracy so that they don't miss but will not hit as hard as another melee with a focus on str, unfortunately that analogy gets murky when haste and food gets thrown in so take it with a grain of salt, please. With a skill setup the Gown +1 is the obvious winner.
A build that is focused solely (or nearly so) on INT offers a different set of benefits. While it is true that INT will offer some MACC thus negating some of what a skill set offers its primary focus is to increase max damage on un-resisted nukes. Make no mistake, you will be resisted more often so don't be disappointed when those Thunder IV's hit for 400 or so damage. When nuking things with low INT totals a super INT build is definitely superior. In this situation the Mortarboard +1 is clearly the best piece of gear that you can obtain for the head slot.
There is one exception to all of this blahblah that I'm putting out and that is helices. The likelihood of sticking an un-resisted helix on anything that is really tough is low enough that you want to make it count if it does stick. There is definitely an argument to be made for increasing skill, but the formula for helices works against us in general.
For a more thorough explanation from someone with far more knowledge than I have please refer to Kaeko's posts
. (He will be missed.)
tl;dr: Situational gear is situational, no one can tell you definitively what is best.