For acquisition of assets, a company acquires another company's assets through direct negotiations or management. Acquisition of stock is when the majority of the outstanding voting shares, usually, is done to acquire control.
With both of these topics, valuation is an important implication. Value of assets and liabilities can be done, usually, by appraisal. Value of potential earnings is done on a "going concern" basis (could be the present value of net cash flows or current earnings). And then valuation for consideration exchange, can be done by cash or securities (with securities, estimated values must be made).
With acquisitions you have to ensure you understand the implications on legal considerations, tax considerations, and ease of consuming stocks vs. assets, For instance, advantages of acquiring assets can include not inheriting a contingent liability or unwanted labor groups. Of course the disadvantages can include the transfer of titles can be time consuming, and the potential that contract transfers are not feasible.
The advantages of acquiring common stock includes easy transfer and reduces the risk of nontransferable contracts. The disadvantages will include the potential pickup of contingent liabilities, labor groups, unwanted assets, and potential difficulty to accessing the target asset's cash.