You haven't specified your team, neither the format. Hence, I will explain for all formats where both Giratina and Yveltal are used.
Giratina's pros and cons:
- Good Defogger, anti Groudon on both formes (Origin forme has Levitate while Altered is very bulky.)
- Able to handle other important Pokemon such as Necrozma-DM, Ho-Oh, etc.
- Major weakness to Calyrex-S meaning you require Yveltal, which has no point to run it.
- Primal Groudon has gone, meaning the main Stealth Rock setter is Necrozma-DM, which Yveltal handles easily.
- Outclassed by Lunala in many ways— Lunala isn't limited to stall as Giratina unlike Lunala gets no good healing except Rest, which means it needs cleric and Heal Bell support.
- Lunala, since it doesn't have a Dragon-type is able to handle Dragon Dance Zekrom, Zygarde and handles every non-Crunch Zacian-C variant.
Yveltal's pros and cons:
- Mandatory on teams that don't have a solid Calyrex-Shadow counter. Indeed, it is one of the best checks to it.
- Threatens Necrozma-DM with it's attacking options, which is one of the most common Stealth Rocks setter.
- Weakness to non-Calyrex-Shadow teams, and loses to Primal Groudon (if it's Nat Dex AG).
- Unlike Tyranitar, it gets reliable recovery in form of Roost.
- Gets Sucker Punch, which is a good anti Caly-S counter and unlike other Dark-types, it is neutral to Pollen Puff.
Run Giratina-Altered if you're running a stall team that has good cleric (Aromatherapy/Heal Bell Xerneas, Chansey, etc.) and a solid Calyrex-Shadow counter and if you have a bad match-up against Primal Groudon (Nat Dex AG only). Or, instead go for Yveltal that doesn't have a Calyrex-S weakness and is able to beat almost all sets of it.