The SEC's bulletin identifies several ways a fractional share can behave differently from a whole one, and each is expressed as something that varies by firm.
Orders may be aggregated. Rather than filling each fractional share order in real time, the firm may collect these orders through the day and then execute one or more large orders. The practical consequence is that the price you receive may not be the price you saw when you placed the order, and the timing of execution is the firm's rather than yours.
Order types may be restricted. Some firms only allow market orders for fractional share investing, so the ability to set a price limit on the purchase may not be available. Market orders and limit orders are covered on their own pages; the point here is that the choice between them may be made for you.
Dividends are paid pro rata. The SEC's example is exact: if you own .75 shares of a stock and it distributes a dividend of $10.00 per share, you would receive $7.50. Nothing is lost, but the amounts are small and, in a taxable account, still reportable.
Voting rights may not exist. The SEC states that you may not have voting rights if you own fractional shares, and that your ability to exercise proxy voting will depend on how your brokerage firm's fractional share investing program works. This is the clearest illustration of the general point: a right that attaches to a share as a matter of corporate law does not necessarily reach the holder of a fraction held in a firm's program.
Liquidity is not guaranteed. Some brokerage firms have indicated that they do not guarantee the liquidity of fractional shares, even if full shares of the stock are liquid. So the ease of selling a fraction is a property of the firm's program rather than of the market in the underlying stock.
They generally cannot be moved, and this is the most consequential one. The SEC's bulletin, under a heading of its own, states that you generally cannot transfer fractional shares to another brokerage firm, and that if you decide to transfer your brokerage account to a different brokerage firm you may have to sell any fractional shares in your account.
That last point has a tax consequence the bulletin does not draw out. A transfer of whole shares between brokers is generally an in-kind movement that changes nothing for tax purposes: the position and its cost basis follow you. Selling a fractional share is not that. It is a disposition, and in a taxable account it realizes a capital gain or loss for that year. The amounts involved are usually small, because a fraction of a share is by definition worth less than one share. But the character of the event is different from what a transferring investor is expecting, and it happens on the firm's timetable in the middle of a move undertaken for entirely unrelated reasons. This is worth knowing before the move rather than after it by anyone holding fractional positions in a taxable account, and it is one of the few reasons to prefer whole shares where the choice exists.
Set against all of that is a real and simple benefit. Fractional shares break the link between how much you want to invest and what one share happens to cost. A $250 contribution can be fully invested in a stock trading at $400 a share rather than sitting in cash, and a portfolio can be built to intended proportions rather than rounded to whole shares. For regular investing of fixed amounts, and for diversifying a small account across many holdings, that is the whole argument and it is a strong one.