Accounting can be done on either an accrual or a cash basis. Accrual accounting recognizes revenue at the point where it is earned, while cash accounting recognizes revenue only when cash is actually received. Percentage of completion is the name of the method used to account for long-term contracts under accrual accounting. It is one type of accrual accounting, not a competing method.
The revenue recognition principle permits entities to recognize revenue on their financial statements when those revenues have been earned and are realizable. Realizable means that there is the reasonable expectation that those amounts to be paid in the near future while realized means that those amounts have been paid. Revenue recognition is one of two accounting principles underlying accrual basis accounting.
The matching principle states that costs should be recognized in the same time period as the revenue that their occurrence helped produce. For example, while a business might only be paid at the end of construction, it should recognize a portion of that expected revenue each time period as it incurs construction expenses. Following the matching principle results in more accurate financial statements and it is the other principle behind accrual basis accounting.
Accounting's purpose is to produce the truest and most accurate portrayals of a business's financial circumstances as possible. Cash-basis accounting attempts to do this by permitting no estimation of values through recognizing costs and revenue only when cash is paid out and received for those amounts. This inevitably produces distortions where businesses engaged in long-term contracts report massively high profits in one accounting period and consistent losses in the others. Accrual basis accounting attempts to remedy this through permitting some estimation of values in order to comply with both the revenue recognition and matching principles.
Percentage of completion is the accrual-basis accounting method used to account for long-term contracts. Percentage of completion does not recognize revenue \when payment is received for the total completion of long-term contracts, but over the term of work on the project. It does so through assigning a portion of total expected revenues to each accounting period corresponding to the portion of total expected expenses incurred in that same period. Percentage of completion forces accountants to admit some estimation into their numbers, but neatly dodges the problem of disproportionate income and losses in different periods.