I'll try analyse the outcome of that battle as non biased as I can by doing two different character studies, and deducting from that who would win. Considering Umbrella Chonicles faces you against various kinds of enemies, I'm only counting the ones below from the main series, bar the Talos and the T-0400TP as they were canologically defeated.
Jill Valentine
Skills: Highly Skilled with a Lockpick, expert in Bomb Disposal, Highly trained Combat Skills, excellent control over various Firearms, years of Military training
Years in service: Was 24 years of age when The Mansion Incident Occured, worked previously as a member of Delta Force. Now works with the B.S.A.A with 11 years combat experience against B.O.W's.
Combat Style: Jill's hand to hand combat skills rely heavily on kicks and acrobatic attacks, with a strong dependancy on speedy stabs when armed with a knife. Her attacks vary from Tae Kwan Dao Roundhouse kicks to Val Tudo Cartwheel kicks, and she is also capable of incorporating excellent gymnastic and acrobatic manouvers into her assaults, as witnessed with her Neck Snap attack. Her army training has encouraged Jill to keep an incredibly toned physique and she has displayed strength beyond that of any average woman her age when she tackled Albert Wesker out a 30 story window and amazingly survived the fall.
Has battled: Zombies, Crimson Heads, Cerberi, Web Spinners, Yawn, Hunters (versions a, b and y), Neptune, Mutated Crows, Plant 41, Chimera, T-002 Tyrant, Drain Demos, Brain Suckers, Sliding Worm, Lisa Trevor, Grave Digger, Nemesis, Talos, Guardian of Insanity, Albert Wesker, Majini (both town type and base type), Duvalia, Cephalo, Executioner Majini, Reaper, Chainsaw Majini, Big Man Majini, Agitator Majini and Bui Kichwa
Total enemies fought that we know of: 34
Other skills: Has a resilient immune system due to the antibodies formed to battle the dormant T-Virus that was within her body, has survived not only the Arklay Mansion outbreak but the Raccon City and Kijuju outbreak too, and is apparently ambidextrous and capable of firing a gun with either right or left hand (as witnessed in the ending for Desperate Escape)
Ada Wong
Skills: Trained in the arts of espionage, Trained Assassin, Trained in the art of Stealth, excellent knowledge of firearms
Years in Service: Currently unknown. Has been working for "The Organisation" undercover since before the first T-Virus outbreak by James Marcus in 1998. Was last seen in action in 2004.
Combat Style: Ada's combat style revolves mainly around flashy looking kicks and somersaults, something which went against her during her interaction with Leon Kennedy in the Salazar Castle in 2004 as her somersault gave Leon the time to draw his knife. Her kicks usually involve a fast, spinning assault on the victim and she is weak competition when armed with a knife. Though she is more comfortable using a weapon than fighting unarmed, Ada is a tactical fighter, known to study her enemy before directly combating them to gain an advantage.
Has Battled: Zombies, Cerberi, Tyrant T-0400TP, Las Plagas, Los Ganados (both Town Type and Base Type), Zealots, Bella Sisters, Garador, El Gigante, Jack Krauser, Osmund Saddler
Total enemies fought that we know of: 13
Other Skills: Ada is prone to using a Hookshot to gain distance away from her foes as well as using it to trip her opponents
Summary
On the basis of skills, years of experience, fighting style and numbers of B.O.W's encountered and faced, it is Jill who walks away from this battle as the clear winner. Having canologically faced more than twice the amount of B.O.W's in her years of service than Ada has, and still living to tell the tale, Jill's battle experience against larger enemies like the Nemesis or Talos imply she's a resourceful and relentless fighter.
However, Ada has shown to rely more on intellect and observation to win in a fight, and as a trained Assassin and Spy her style of combat naturally would not rely on direct confrontation but more of a ranged nature. From a distance, Ada seems to be at an advantage, and this can easily be reached if her Hookshot is capable of shooting to a higher platform. Considering Jill is an expert with various weaponry, distance could easily be covered with a Sniper Rifle. This battle would ultimately be won via cunning and intelligence, which seems to be more suited towards Ada's fighting style.
In a direct confrontation, with no weapons, Jill's combat skills are far superior. Her attacks are hard hitting, fast, direct, and varied in comparisson to Ada's flashier and almost non professional style. When armed with a knife, Ada again falls to Miss Valentine due to lacking speed with her knife strikes (compared via their stabbing motions in Resi 4 and 5).
In conclusion, Jill is the winner in a direct combat situation, as well as a being a better survivor and soldier with her former experiences and defeated B.O.W's. Ada's only chance of winning the battle is to rely heavily on keeping a distance away from Jill and relying on the stealth and analytical aspects of her espionage training.