What kind of structure?
What kind of building do you intend to cover with the new roofing? If it's a small shed or other outbuilding, then you've hit on the one area where you genuinely do have a choice. Roll roofing is usually a good, economical pick for this use, whether the roof is flat or pitched. But on sloping roofs on sheds and outbuildings, shingles would also be entirely acceptable, more aesthetically pleasing and more long lasting (and more expensive).
What kind of roof?
If you are looking at a house, then the answer depends on the type of roof. If you have a flat or nearly flat roof, then shingles are not the answer because they will not keep out the weather--ice and water may back up underneath them. In fact, code specifies a slope of at least 2/12 for all shingles, and good practice calls for special installation techniques on slopes between 2/12 and 4/12. In this case, rolled roofing is one answer (but note that there are longer-lasting and more robust alternatives to asphalt roll roofing, such as membrane roofs). One of these may make more sense in the long run).
If your house has a sloping roof with a pitch of 4 in 12 or steeper, roll roofing is not an option (but there are, of course, other alternatives than shingles, such as a metal roof). It is less effective, less attractive and in any event probably not permitted by the building codes in your area. In this case shingles of some kind are a good choice and the standard in most parts of the US.
Before purchasing roofing materials, always check your local building code because different codes have different fire-proofing requirements. Once you have installed your roof, maintain it well and keep it clear of debris.