It's mostly a convenience factor.
I've never played gestalt, so this is solidly in the realm of theory crafting. The fact that this is E6 definitely changes things, as having to dual-scribe (in the sense of "I learned this as a wizard/arcanist spell, so I'll copy it from myself as an arcanist/wizard spell") any spells a caster wants available to both classes gets a lot tougher at higher levels as page and gold costs scale up.
Ultimately, this isn't a direct increase in power, as the caster can always just scribe between their two classes. This is taking a freebie/trait/feat to save time, money, and carrying capacity, which is tough to directly compare to traits and feats because it combines so many aspects. Rich Parents is a trait that increases your starting gold by ~830gp, which is enough to buy two additional spellbooks and pay for dual-scribing 8x 1sts, 6x 2nds, and 4x 3rds with 120gp left over. Those additional spellbooks are only 6lbs extra, which all but the feeblest wizards could probably handle (and if they're cross-scribing 3rds, they're already level 6).
Spellbooks are pretty roomy at lower levels.
Take a level 6 wizard/arcanist gestalt. If they always took new spells from the highest level they could access, they would have (cantrips are variable due to "begins play with a spellbook containing all 0-level wizard/sorcerer spells" and 10 of those cantrips coming from a blog or being very niche and non-PFS legal):
- Wizard: 25-35x cantrips, 5x 1sts, 4x 2nds, 4x 3rds
- Arcanist: 25-35x cantrips, 7x 1sts, 4x 2nds, 2x 3rds
At 1/2 page per cantrip and one page per spell level otherwise, the 6th level wizard needs 37.5-42.5 pages and the 6th level arcanist needs 33.5-38.5 pages. Combined, that fits in 71-81 pages, so they'd need to be picking up quite a lot of additional spells to have overflowing spellbooks at early levels.
This mostly saves gold and time.
Let's assume that the character in question would like to have solid parity between their wizard and arcanist spells and are making the decision between dual-scribing half of their spells and taking this as a trait or feat. How much value do they get out of it? To put some arbitrary numbers on it to try to quantify the value, let's say that they:
- Always take new spells of the highest level at levelup.
- Purchase and scribe six additional spells past first level, all at maximum level.
- Want to dual-scribe half of their spells from each casting class (e.g., they won't bother to dual-scribe Mage Armor), except for cantrips.
- Only bother with 25 of the 35 potential cantrips (add +10 pages to the totals if they really max them out).
At the following levels (choosing levels where wizard and arcanist have the same maximum spell level to allow for maximum dual-scribing), they'll have:
- Level 2: 50 cantrips, 24x 1st; 49 pages
- Wizard: 25 cantrips, 5x 1st
- Arcanist: 25 cantrips, 5x 1st
- Purchased: 6x 1st
- Level 4: 50 cantrips, 27x 1st, 27x 2nd; 106 pages
- Wizard: 25 cantrips, 5x 1st, 4x 2nd
- Arcanist: 25 cantrips, 7x 1st, 2x 2nd
- Purchased: 6x 1st, 12x 2nd
- Level 6: 50 cantrips, 27x 1st, 30x 2nd, 27x 3rd; 193 pages
- Wizard: 25 cantrips, 5x 1st, 4x 2nd, 4x 3rd
- Arcanist: 25 cantrips, 7x 1st, 4x 2nd, 2x 3rd
- Purchased: 6x 1st, 12x 2nd, 12x 3rd
Even by level 6, having bought 30 additional spells and scribed them, they're not quite filling up two spellbooks. The dual-scribing is more of a time and gold sink than anything, dual-scribing and costing a total of the following:
- Level 2: 8x 1st; 8 hours and 80gp
- Level 4: 9x 1st, 9x 2nd; 27 hours and 450gp
- Level 6: 9x 1st, 10x 2nd, 9x 3rd; 56 hours and 1300gp
It comes down to how valuable that is in the campaign.
In some campaigns, having to spend multiple days and hundreds of gold dual-scribing spells into a second spellbook could be non-viable. In some campaigns, it could just be a downtime activity. It's definitely of non-negligible benefit in terms of convenience and cost, but outside of an aggressive timeline and scarce resources, it's not going to make or break much.
Personally, I'd put it as a trait. I like the idea of it not being free because it says something about the character — it's like a shorthand-specific form of Mystic Theurge. They haven't married two sources of magical power, but they have figured out a unified shorthand that they can apply to two separate sources of magical power. It saves some time, gold, and weight (although a Blessed Book would negate the latter two), but unless the mage wanted to cross-scribe every spell and was picking up oodles of new spells, I don't think it's impactful enough to warrant a feat.