Well, if the Jackals are snipers with 1S1K (1-Shot 1-Kill) beam rifles, then the Jackal has a good chance of killing the Elite.
That's actually a pretty tough matchup, which I am rather surprised to say. Kig-Yar are, like, really good snipers, and Sangheili are awesome leaders, assaulters and are athletic. So, I think it depends on the quanity of each alien race. If there are more Kig-Yar than Sangheili, Kig-Yar, but with more Sangheili than Kig-Yar, Sangheili.
ok hold a second. jackals cannot 1S1K elites because they have energy shields and FYI the elites did go up against jackals and the rest of the covenant with only a handful of human survivors with them and they won so there you go