Chris Ivory is a capable starting running back. He led the Saints in rushing as a rookie and made the NFL all rookie team. When he went to the Jets he had a couple of 800 yard seasons in a committee with Bilal Powell in 2013 and Chris Johnson in 2014, and when he was given a heavier workload he led the AFC in rushing in 2015. So the guy has a decent record. Is he a top tier running back? No. He is not a back that will have much success behind an under performing O-Line. He isn't Adrian Peterson (in his prime) or Zeke - those guys could have come into Jacksonville this season and had really productive years. For a guy like Ivory to have success he will need help from his O-Line and a commitment from his OC to the run. Is he good enough to start for us next season? Sure, but he will always only be a steady running and not a special one.
As for Yeldon. I am not convinced he is a feature back in this league. He strikes me more as a pass catching back, who can handle some carries, but not a heavy workload. Is he good enough to work in a one-two punch with Ivory? Sure, it can work. But the team would need to commit to feeding Ivory the ball and using Yeldon as the pass catching back. If we moved forwards with this duo there would need to be a belief that they can stay healthy and produce behind an improved O-Line. Is that a risky thing to do? Perhaps, but by sticking with these two (plus any other additions to the running game through free agency or the draft), then the team does have enough on this roster to have a productive running game. However, we don't have a back that will do for us what Zeke has done for the Cowboys, or Johnson has done for the Cardinals. We have steady backs, not special ones like we had with Fred Taylor and MoJo.
What would I do?
I would honestly consider drafting Fournette or Cook in the first round. I know some don't like first round running backs and would want to see us use our pick on a different position - I get that, but we have all seen the impact that Todd Gurley made as a rookie last season and the impact that Zeke made this season. Take Zeke away from the Cowboys and they would not have won as many games as they did, nor would their offense have been anywhere near as prolific as it has been. When you get the chance to draft a special running back, then that could be a very appealing thing for this team. Remember that we have put this team on Bortles' back in the last two seasons. Imagine what Zeke could have done on this team. Suddenly we have a special back we can feed the ball to 20+ times a game. That would take a ton of pressure off Bortles and he would probably be better for it because we wouldn't need him to do everything. So far as I'm concerned, if we believe that Fournette or Cook are potentially special running backs (I'm not talking solid backs coming out of college like Trent Richardson), then I would have no issue seeing us draft one of them because they could help take this offense to the next level.
Obviously we have other considerations to make. But our defense is talented and isn't that far away from being good. We can add prospects for the D-Line, linebackers and secondary in the other rounds. Not every star defensive player has been taken high in the first round. Richard Sherman was a fifth round pick, Kam Chancellor was a fifth round pick, Bobby Wagner was a second round pick, Frank Clark was a second round pick, Jarren Reed was a second round pick, and KJ Wright was a fourth round pick. Now I appreciate the Seahawks are one of those rare teams, but the way they have drafted proves that star talent can be found in any round. So we don't really need to worry about drafting a DE or S with our high first round pick if we feel that adding a special running back could make a greater impact, and we could add a DE or S in another round.
For me, I would grab Fournette or Cook. I don't know which guy I would pick. I think Fournette has the edge as a runner, whereas Cook is a better all round back due to his pass catching ability, but both should have a ton of success in the NFL. I'd love to see us get our next special running back.