I would recommend "company's business". (Unless you meant a different context...)

For example, "the company's business is to sell cars."
Business means the company's core activity, related to its main objective and seen as a whole; thus it sounds more straightforward.
Operations may mean the same, but often also the [internal] functioning/operating, <I>running of the business</I> ('the method or practice by which actions are done' - http://en.wiktionary.org/wiki/operation), or certain parts of it ("If sales are down, you must first consider a problem in the operations side of the business (i.e. delivery, customer service, quality control) before you spend money on any kind of advertising." - http://hubpages.com/hub/Marketing-vs-Operations-Cant-We-All-... ).