profit center accounting is basicaly done for internal controlling purposes. It lets you determine the profit and loss using the cost of sale approach or period accounting approach. Here you can find the profit from an "area of reponsibility or pserson" point of view.this is accound based costing
Whereas in Profitability analysis, market segments based on product , cutomer,order aor any comobination of these are studied to find wots the profit. PA provides information to the marketing,sales and planning department so that they can make decisions. PA has two forms account based and CO based.
both these are tools for profit managment, and both are alternative. They are not same.