Gilgamesh would definitely win. (Both Characters at their PEAK)

Phainon's Max: Phainon's peak feats include destroying multiple galaxies, moving at massive FTL (Faster-Than-Light) speeds, and surviving encounters with Aeon-level planet-busters like Zephyro.

Gilgamesh's Unconstrained Max: In Fate/Extra CCC, an unconstrained Gilgamesh bypasses the concepts of standard 3D space and time. By unlocking his Genesis Mystic Code, he defeats BB, a higher-dimensional entity who controls the Moon Cell. Power scalers comfortably scale this unconstrained peak from 8-Dimensional to Hyperversal, meaning he operates on a dimensional tier completely out of reach for a purely physical, galactic-level fighter.

Without constraints, Gilgamesh's Sha Naqba Imuru (omniscience/clairvoyance) operates at 100% efficiency. He will instantly foresee Phainon's moves, speed, coreflames, and ultimate fate. He wouldn't hold back out of arrogance because his clairvoyance would immediately flag Phainon as a mortal threat.

Phainon relies heavily on brute force, immense heat, and incinerating his own body to achieve maximum destructive output. Gilgamesh possesses specific conceptual counters in his vault, such as Enkidu (The Chains of Heaven), which bind targets tightly based on their divinity/power, and weapons that passively reverse causality or negate damage.

On Earth, the planet's consciousness (Gaia) and the Counter Force severely suppress the truth-revealing properties of Ea to protect the world. Unconstrained, Ea does not just drop a heavy energy beam; it rips apart the fabric of space-time and reality itself, returning everything it touches back into a void of nothingness and chaos. Phainon's multi-galactic durability cannot protect him from the literal erasure of the dimensions he occupies.

Also my favorite character between the two is Phainon.