What is the difference between the Chantry Garden and the Herb Garden upgrade in Skyhold?
You can find this information on the Dragon Age wiki on the "Major Upgrades" page.
If you choose the Herb garden :
- you have six pots instead of two to grow your plants, meaning you can grow up to six at the same time
- they do not grow faster nor is there any other advantage over the Chantry garden ; though if you craft a lot of potions or want to go for the Botanist achievement (harvesting 50 plants from Skyhold garden), it is much more convenient
- you get a codex entry for Skyhold Garden
If you choose the Chantry garden :
- you keep your two herb pots, meaning you can still grow herbs, only slower
- you get a Chantry Banner crown
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you get a codex entry for Skyhold Garden
The "resource gain from the inspired" and "gold from tithes" refer to three war table missions that get unlocked:
- a War Table operation called "The Archive of Montfort", which rewards you with a Masterwork Balanced Pommel (reward info found on SegmentNext, not the wiki) and is faster when completed by Josephine
- a War Table operation called "Tithe of the Faithful"
- a War Table operation called "Eyes of the Maker", which rewards you with a Gold Bracelet
Despite that, the upgrade is mostly a cosmetic one. The benefits gained from one or the other garden are minimal at best.
There are certain game options only available to an Inquisitor that embraces being a religious figure (for example, being able to convince the Grey Warden Ser Ruth to accept forgiveness in the Skyhold Judgement). The Chantry Garden war table missions are one such option.
If you have the Chantry garden and are a "faithful" Inquisitor, you will unlock a few war table missions. If you're not "faithful" (you've said in conversation you weren't saved by divine intervention etc) those missions won't unlock even if you have the Chantry upgrade.
The Herb garden gives you 6 pots to grow herbs. The Chantry garden gives you 2 pots for herbs. They grow at the same speed.
This is all the information I've been able to discover by playing. I have not seen any reference any "resource gain" by playing.