Raikou or Gilgamesh?

Raikou

Go for mama raikou
I assume you have a mlb dragon's meridian (gives 50% starting NP), pair that with support waver you can fire your np at the start, or hold it till the boss phase
Also, she has mystic slayer which gives bonus damage to almost everything in the game and a dodge in 2nd skill.

Go for your favorite. Gilgamesh is overall better for hard content because servants are frequent enemy on those, but Raikou also gets bonus damage against a lot of servants and troublesome monsters which can be insanely useful for farming...like those Dream Eaters and Demons from the Hunting Quest. The sad part is that Riakou's NP doesn't have an interlude just yet, so it's stuck at 300% for a very long time.

Only go Merlin if you don't want to think anymore. If you enjoy hard content and strategizing, avoid Merlin at all cost...and it's not like you will have a hard time finding Merlin on support. Later on he will become scarce though, because people prefer to have Waver or Skadi as Caster support (they have way more farming utility).

So yeah, Merlin is a cheatcode and Raikou is more useful than Gil, but i'm biased.

If you want to clear waves/farms without thinking about most of the class systems in general, both can offer you easy farm mode, using Dragon Meridian/even NP battery CEs is enough.
Good thing about Raikou and Gil is, they're too good as a servant.
Can slay multiple servant bosses using their NP and wreck single Bosses using high Buster Crit damage.

Good choice on picking one of them, if we realize there are really few servant who can cover ST and AOE roles like Gil and Raikou.
3 in 1 simple yet effective.
Both is fragile, by using a team that thing can be covered.

I choose Raikou, it's because Buster Crit Zerker with magnet skill + Mana Burst and Special damage is too awesome.

Though the choice is still up to you, no matter who you choose both is a monster to begin with.

Raikou, as someone who have raikou i can asure you that she is monster, with righ teammate you can bring her almost anywhere. Righ now no one can clear wave and kill boss better than raikou. her Np damage wont really great if your enemies isnt a sky, eart servant or devil but its still big and she can create around 20-50 star after np

Raikou

Personally I like Gil better gameplay wise but Raikou's probably better for farming purposes. Btw, Gil's NP battery skill already came like a while ago.