Gil Caster and Paracelsus and what's their in depth advantage and disadvantage?

It's definitely recommend to roll for Cas Gil he is much better than Paracelsus at everything (except giving guts but the long cool down on Paracelsuses Guts skill makes its unreliable)

The damage of Paracelsus is non existent Cas Gil on the other hand can do some neat damage even his NP is anti Amy and anti fortress.

Paracelsuses has only one advantage that is he is a 3* and easy to obtain and requires less exotic ascension materials.

As far as their art support potential, that is tied to one skill for both of them, and Gil's is the superior one by far. Both of their skills do essentially the same thing: increase arts effectiveness for their party for 3 turns. However, Gil's does so for 30% on a 6-turn cooldown, while Paracelsus does it for 20% on a 7-turn cooldown. Gil's arts buff also comes with an enemy debuff success rate increase, so Gil would make a good companion to any servant that has lots of debuffs, like Hassan of the Serenity or Shuten Douji.

Aside from that, their NPs are both arts AOE, but Gil's hits harder (450% vs Paracelsus's 400% after strengthening), though you should note that it'll be much easier to get Paracelsus to NP5. Even then however, Paracelsus's NP is only stronger than Gil's by a little bit, and Gil's ordinary attacks deal much more damage, so the comparison still favours Gil.

Gil's NP also arguably has a better secondary effect: lowering enemy defence, while Paracelsus's NP lowers their attack. As for the rest of their skills, Gil has a party-wide crit star gen boost and party-wide attack boost, while Paracelsus has a self-NP battery and a targetable guts. This will be strengthened to include an NP gen buff too, but that'll happen 2 years from now. Overall, Gil has more supportive skills that help his team deal more damage, while Paracelsus has a slight focus on helping his team survive with guts and enemy attack reduction.

Additionally, their NP gain is generally comparable: Gil's base gain rate is quite low, but he compensates with 5 hits on his arts cards and 10 on his NP (his NP gain with his NP is halved though). Paracelsus's NP is average, but his hitcounts are quite low. This means that Gill will generate slightly more on his arts cards, while Paracelsus will generate more with his quick and extra cards. Since they both have 3 arts cards though, I'd say Gil comes out slightly on top.

Finally, factoring in their stats as 4 and 3 stars respectively, Gil ends up clearly superior. All his skills are party-wide, his arts buff is objectively better, and his emphasis is on helping his team deal damage. Paracelsus is kinda like a budget Gil caster: poorer base stats, poorer (but still good) arts buff, and his only party-wide buff is his arts buff, of his other skills, one is self-targeting, and one is selective targeting, and he places a greater emphasis on keeping his teammates alive.

Paracelsus's biggest flaw imo is the longer-than-necessary cooldowns on all his skills. His skills are good, but their cooldowns mean that most people tend to go with other servants for support, since without his skills he is very lackluster. He's still useable, but Gil is just much better than he is.

By the way, just saying, but if you want an arts support, why not just roll for Tamamo on the Halloween rerun that's coming up next week? She's best arts support after all.

Rolling for Caster GiIl in Babylonia Chapter release means that pool you also have chance to get excellent SSR servant (Enkidu, one top Lancer) and specific SR servant (Medusa Sister anti-Male), and top-class SSR and SR CE.

Basically Caster GIl is one top Support caster and a servant has ability between SSR and SR because of (1) NP combines support+AOE damage and (2) King's Return is quite unique skill, even though its cool-down is long. And (3) all skills and NP effect are FOR TEAM. So the combination effect is really great.
For instance, although Art card is "~0 star generation", but when his King's Return activated, his NP and Art card can also generated tons of Stars. You also should understand how important for NP gain of Critical Art cards. When in combined with Sovereign of Magic Wands, other servants with high-hit account Art card (and NP) could be highly benefited.

And like his Sovereign of Magic Wands, well dont forget that this skill can also bring 30% debuff successful rate, which means other teammates' Debuff skills and NP could be highly benefited, like Curse, Charm, Stun, etc. Like your Mozart's NP effect.

In some cases his works good for Art-oriented Assassin versus Rider even better for Tamamo. you can check this gameplay as one typical example:
https://www.youtube.com/watch?v=tKDWD1D-l3o
Even though Caster Gil could be defeated by Riders quick, but all his buffs (And Mozart) can help Kiritsugu until 5th turn and solo the boss for the final 3rd HP bar.
83 stars of Kiritsugu's NPBAe and NP spam (with Mozart's help). It is almost impossible for any other support.