Gil trying to hit on Ragyo.....whoa. ^^;
Also technically, Gil is actually only High 7-A like Ragyo when using Enuma Elish. But it's whatever.
I feel that Ragyo may take this more due to higher stats, regen, and of being an actual, better fighter than Gil AFAIK of her to him. While she doesn't the vast weapon variety as the King himself and doesn't have something else like his precog and her mind control power being negated by his willpower (that'll work?) and his armor granting him even further resistance to it (which likely will null the mind control....mmm), Ragyo still feels like she can take this as Gil's very likely to not use anything other than GoB and maybe his Virmana.
The potency of the weapons from the GoB range from City to Mountain level, something that Ragyo is likely fine of taking given her much higher stats (even Berserker'S God Hand had a limit to handling against the many barrages from GoB). Gil's only option her would be if he chip-damaged Ragyo with his strongest weapons which he may likely not do right away. Even then, it's more of if a massive barrage of 7-A level weapons can pierce a High 7-A being like Ragyo. I feel that it COULD work, but only barely at the most. Even if she does get hurt, as long as none of them were ones that can f up with regen, Ragyo would heal up from any of those injuries (even if minor).
CQC is a no go as Ragyo is physically much stronger than Gil whose only Class PJ physically by his physical strength outside of his GoB. And it'd be worse once he gets gripped by Ragyo, where she'll either choke him out or otherwise (whatever she would likely do to a person like him). Gil could get up in the air and bombard Ragyo from afar (will just likely result in the same as above given her dura). But Ragyo also has her own form of flight that she can use to catch up to Gil in the air, so there's no safe spot for Gil in the air either.
The only way i see Gil even winning would be if he uses Ea and Enuma Elish, along with perhaps using Enkidu to restrain Ragyo in place for a bit. Even then, Gil using Enuma Elish would pretty much be the non-fullpowered one. Though even when finally using the only thing that can remotely injure Ragyo, Ragyo still has regen to heal from the damage. And since Gil is not likely to ever use EE at fp, he's pretty much f'd by either a punch (since his armor only protects him to up to 7-A level, which Ragyo is above that by a whole tier), or just forced to play chicken and do hit- and runs at her for a while.
I'm going with Ragyo here.