If your goal is to save on interest, I'd hit the highest APR debts first, or the ones you're paying the most interest on. All else equal though, I'd hit the credit cards before the installment loans since (a) the APRs are probably higher, and (b) high revolving utilization is keeping your scores down.
If you're seeking a consolidation loan, I'd pay off the credit cards, get them all to zero except one which reports a small balance--this will boost your scores for qualifying for the loan. Then get the loan, pay off the rest of your debts, and then pay toward the consolidation loan.
Another option is to pay off the credit cards, then use the additional $1300/month you're freeing up to make a bigger dent in the installment loan debt. Make sure your loans can be prepaid toward principal before paying extra on them.
The discussion has broadened far beyond OP's original question:
"Would paying off my credit cards or loans first provide the biggest FICO boost?"
The answer is paying off credit card debt would provide the largest FICO boost.
If that is OP's only concern, the rest is a moot point.
OP also said the end goal was to take out a debt consolidation loan. IMO, paying off the credit card debt with cash-on-hand would boost FICO and make lenders more comfortable in approving a consolidation of the installment loan. During underwriting, that revolving debt involves a much higher risk assessment than the installment loan debt.
However, if OP would like to bring other variables into the discussion, there are some excellent points. Many of us on the forum would consider the lowest cost or quickest way to repay substantial debt, but this might requires disregarding FICO impacts in lieu of saving money or time. I think @CL-Addiq makes some excellent points and we would need to know more details to help @Cpmcmxc fine-tune debt repayment. In general, paying off credit cards first would normally be the way to both boost FICO score and also save money since credit cards typically have much higher APR than installment loans. However, there are exceptions in both cases. The question about what kind of installment loans we're talking about also matters. Are these loans a mortgage loan, a student loan, a car loan, a small business loan, or a high-APR payday loan? What are the terms on each loan? How do they compare to the terms on credit card debt? Is saving money on repaying the debt even a concern for OP?
@CL-Addiq wrote:To give the best advice, one would need to know all the variables.
What is the nature of your cash flow?
You're currently paying about $2.7k a month in debt servicing. Presumably, this is after paying necessities like food and shelter. Is this sustainable, or is your income seasonal or in some other way at risk? Is your total credit card debt going down or are you just paying the minimums?
Is the loan secured or unsecured?
If the loan is secured against say a truck then the impact to your credit is probably negligible. The loan can be recouped by just seizing the truck. However, if that truck is required for your job then securing your livelihood might be a more important goal than minimizing your credit score.
Does the loan even allow prepay?
I had a student loan which did not and I paid a big chunk of money only to discover I didn't save a penny of interest and lost out on hundreds or even thousands of dollars of investment potential.
What are the interest rates?
If you have a 0% or low intro rate, it might save you money in the long run if you put the money in an interest bearing account for now and paying it off once the intro is over. Otherwise, generally you want to pay the highest interest first.
What is your credit card utilization?
AZEO is generally a good score hacking technique, but I think if the one card is at 90% then you're probably better off spreading it out over a few cards.
I know your stated goal was maximizing your credit score. I also recommend trying to keep enough cash on hand to cover 3-6 months of expenses. You might be able to do this while also significantly increasing your score.
Totally agree with @Aim_High and @CreditMarathoner . I'd like to add that credit card utilization makes, or breaks scores. To maximize scores? No brainer... pay off the cards.
However I'd eat froot loops or rice and beans for a while to payoff that remaining $30k. That's a high payment for the balance if it's not a nearly done mortgage.
