Benefits of quests after destroying the Diamond Weapon

Solution 1:

Below I list both areas, as well as the Materia/Weapons/Limit Breaks you can acquire. Note that you need to do the Materia Thief Side Quests in Wutai prior to starting disc 2, but you can do the second part of it anytime after that.

For the record though, if you are trying to get the Enemy Skill "Trine" for all four of the games "Enemy Skill" materia, you will need to wait to do the second part of the Wutai chain (The Pagoda) until after you have all four materia. Then, when facing Godo, you will be able to collect the skill on all four materia.

Sunken Galinka

This area has some great materia, as well as as Yuffie's Ultimate Weapon: The Conformer.

Materia found in this area

Double-Cut

Hades (Awesome to pair with the Added-Effect materia)

Limit Breaks

Highwind (Cid's Final Limit Break)

Ultimate Weapons

Conformer (Yuffie)

Wutai

This area also has some rare materia, as well as Yuffie's Final Limit Break.

Materia found in this area

First time doing the side quests (Materia Thief)

MP Absorb

HP Absorb

Second part of the side quest (The Pagoda)

Leviathan

Limit Breaks

All Creation (Yuffie's Final Limit Break)

Conclusion

In case it wasn't clear enough from this huge list of items, since the areas and the side quests are relatively small (but do require decent preparation at least for the Yuffie side quests), I would definitely consider it "worth it" to go back and do them.