The major difference between these two sources of funding is the retention/loss of owner equity. You like owning your business... right?! We do too. Grants do not require you to give up any personal equity, or ownership, to access funds. This means they are a non-dilutive source of funding.
Private investors, on the other hand, require equity, a piece of your business, to balance the risk associated with their capital contribution. In other words, for them to provide you with money today they need to own some of your company until a reasonable exit path becomes available. The amount of equity taken will be determined by a valuation of your business!