Any Chase balance won't affect the Bank of America balance. Your credit reports will be updated within a few days of both statement balances closing (or any time that a Chase Card is paid to $0).
Are these your only two revolving accounts? If you are trying to maximize your score, it's difficult to manage that with 2 cards. Depending on the statement balance reported, you will either receive a penalty for 100% of your cards reporting a balance or (likely worse) none of your cards reporting a balance. You could of course manipulate that a bit by both letting the Bank of America card always report a small balance at statement close and always paying your Chase Card to $0 the day after your statement closes.
I do not think this would have much of an impact on scoring as long as one is reporting at the 6% theshold for utilization. Always pay by due date and not closing date.
Starting Score: 544
I know this is not one of your thesholds from past posts @Remedios however, Experian states that 6% is utilization lenders like. All sources have different numbers and according to my report, anything said is general information.
@tricie17 Experian doesn't create FICO scores; Fair Isaac does based on information contained in consumer reporting agency data (such as Experian). The exact metrics used in determining those scores is proprietary information, but years of repeatable tests on these forums shows the numbers arrived at and commonly used here to be correct.
The exact quote on the Experian page you are referring to is, "In general, always try to maintain a ratio of 30% or less to avoid hurting your score. For top credit scores, keep your utilization under 6%." This is factually incorrect, as there are well-known scoring penalties for 10% or more and 30% or more utilization (and the reason you will usually see those as 8.9% and 28.9% is that 9.000000000001% rounds up to 10% and causes a scoring penalty). The amount of any scoring penalty will differ with every profile.
I do not refute the validity of FICO vs Experian however the infomation is in general. Although Experian is one of the bureaus using information from peoples credit files to infuse with FICO, the scores are FICO. Now there are Vantage scores in which each bureau project which makes things even more confusing and to top off their topsy turvy scoring, the scores are fairing for some companies. This is an ongoing subject and each file is different. Albeit, I understand your post @K-in-Boston