Chase doesn't care about relationships unless you have buku bucks with them. I would probably hold off on the Chase until your scores are better. CLIs are a HP and if you get approved at a low starting limit, it could be hard to grow. The prequal page will prequalify you even if you're over 5/24, so that should show how reliable it is. On the other hand, if you log in and it's in your offers as pre-approved, it's basically gauranteed. The only way to be more sure is to go into a branch and ask if they have any offers for you. I'm currently pre-approved for the CFU while being at least 9/24. I just won't apply because I don't need another $1k limit. I'll wait until my profile is in better shape.
I'm bias. With that said, I believe this is a comparison of apples to a Turkey dinner. I will be the advocate to go for the Freedom card- which retains an actual value vs a builder card that is often bucketed before you apply. If I'm to consider each card for growth, the answer is obvious. Perhaps, not without effort, but anything worth something takes work.
IMO... I would go the Chase route for your future growth, but would suggest you wait until your scores are higher. That way, you would benefit from better starting terms and a higher SL. Once you start getting away from sub-prime cards, your options continue to grow... good luck!!! 
“Most people work just hard enough not to get fired and get paid just enough not to quit.”
To follow on the other posters, the Capital One Platinum is more of a starter/credit builder card with minimum benefits and no real long term rewards. Often Cap1 buckets people with this card and to take three Hard Inquiry hits in the credit bureaus can be a hard pill to swallow. All that being said, Cap1 has given many of the posters on the MyFico Forum a new beginning.
The problem may come later when you are ready for the regular credit cards. Cap1 often will offer better cards but not always. One of those YMMV things. Started with the Cap1 Platinum in the steps program (three steps) and after several years (eight years to be exact) of being stuck at $750 credit limit and no options to move to other Cap1 Cards, I shut Cap1 down and never looked back. 
Good luck on your choices.
Will add the JP Morgan Chase Freedom and other Chase Cards offer Ultimate Rewards that are at the top of the heap in value ... there real competitor is the American Express Membership Rewards.