People who compare Jiralhanae and Sangheili in general, then list the features of the highest rank ground-based Jiralhanae. I believe this is somewhat a logical fallacy. People seem to miss the sheer might of Field Marshals. Field Marshals are literally one rank below Supreme Commanders (as the two positions often thought of as between, Shipmaster and Fleetmaster, are actually "titles", not ranks. There is even a case of an Ultra gaining the title of Shipmaster. An Ultra jumping to the commonly held status of Shipmaster is inconceivable due to the Sangheili rank-system if it were truly a rank).
Let's talk about what each rank actually means:
• Field Marshal: a member of the "Zealotry", Field Marshals are the highest rank of ground-based Sangheili forces. Due to that fact, it can be assumed that Field Marshals have at, or higher power than those typically attributed to the "Field Master" title in the original trilogy. Field Masters have command over at least a battalion of warriors composed of a variety of species.
• Jiralhanae Chieftan: the third highest rank in the Jiralhanae hierarchy, Chieftans are given command over a pack, typically consisting of half-a-dozen warriors, typically composed of Jiralhanae, but sometimes lower species such as Unggoy.
Clearly, Field Marshals outrank Chieftans by a great deal in the Covenant. thankfully, both species' ranking systems are almost identical. To rank up, you need to kill stuff. For Jiralhanae, this is simply a kill-count, including unarmed civilians, children, and possibly indigenous animals (however the latter is unlikely). For Sangheili, their rank is based on honorable kills. That means that each of their kills counted is against an armed opponent in at least somewhat fair conditions. Due to Field Marshal's higher rank and harder requirements to get there in the first place, the Sangheili Field Marshal is clearly much more deadly, at last against Humans.
I am giving overall combat ability to the Sangheili Field Marshal.
In strength, Jiralhanae clearly have the advantage. There is no example of any Sangheili ever physically overpowering a Jiralhanae of equivalent rank. Despite the Field Marshal's higher rank, I doubt the Sangheili would be close in terms of physical strength to the Jiralhanae.
In tactics, Sangheili are often found to be better tacticians, making effective use of troops, equipment, and geography. Jiralhanae in general fail to make any tactical decisions, aside from a very basic grasp of strategic protection.
In usage of weapons and technology, Sangheili obviously get this one, but not at fault from Jiralhanae. Being as the Jiralhanae are a new race to the Covenant, and the Sangheili much older, the Jiralhanae had much less experience with Covenant equipment overall, as well as restrictions placed on the Jiralhanae by the Sangheili, as shown in most naval engagements during the Great Schism.
In speed and agility, this one is more interesting. Typically, Sangheili outclass Jiralhane in agility by a long shot due to Sangheili culture and training. However, as the rank of Jiralhanae goes up, they are often found to be much faster than their pack-mates, and even most Sangheili. Since this is strictly between a Field Marshal and Jiralhanae Chieftan, I am going to say this is a tie, only because of the sheer prowess that is needed of a Field Marshal (Especially as a Zealot-class).
So overall, Sangheili are better combatants, and in a random fight between a Field Marshal and Jiralhanae Chieftan, the result would likely be a Sangheili victory. However, since specific weapons and scenarios are given, I think a more specific answer is needed.
In CQC, the Chieftan has the advantage solely because of physical strength. Despite likely being slower in terms of striking speed and reaction time (running speed is a bad indicator for either), it's likely enough to hold out for a half of a second or more (enough time for a skilled CQC combatant to deliver a strike), allowing the Chieftan's massive advantage in physical strength. Although the rank of the Sangheili is great enough to show that this scenario will not yield a Chieftan victorious every time. The weapons provided for each are also more in favor of the Chieftan for this scenario.
In ranged combat, the Field Marshal has the extreme advantage due to Sangheili's accuracy, and because the overall combat ability of the Field Marshal. That combined with the better familiarity with equipment, better strategic planning, and weapons slightly in favor of the Sangheili for the ranged scenario, the Field Marshal will emerge victorious every single time.
Edit: I misread "War Chieftan" as just a regular Chieftan. After further research, I've come to the conclusion that the results of the two scenarios remain the same, now with only a slight chance of the War Chieftan winning the ranged match due to his shields.