Both FI and CO result in reported lists of (amount) totals. FI has always been considered external or GAAP (today US and IFRS, depending on HQ location) accounting and CO internal or management accounting. Functional Areas however are part of FI and result in variable costing view of income or which costs originating in responsibility areas like manufacturing, marketing, research, management, etc. are covering sales effected by the legal entity. Value fields on the other hand exist only in CO module and are only fact values (quantities or amounts) that are aggregated summarized depending on the intersection of characteristics (dimensions in OLAP). Both functional areas and value fields are part of Income Statement and group I/S accounts and cost elements (secondary after assessments) and result in bottom line amount.
Both FA's and VF's are part of OLTP model, but are better supported if transferred to multidemensional OLAP (BW, BO, Excel, Browser). Once reconciled with submodules (and subledgers) from SD, MM, HR or AR and AP the amount totals can be easily manipulated (pivoted) inside an Excel spreadsheet or browser.