Above all other decissions to make when choosing your new roof type, you must decide on a budget. How much are you willing to spend on a new roof. On a typical 1700-2100 sq. ft. roof (we will use this sq.ft. as an average for all comparisons), you can expect to spend $2k – $15k for the various types of asphalt shingles. For concrete tile expect to spend between $17k and $60k depending on specifics. Slate tile can run as much as $84k depending on the quality of the slate. Steel roofing might set you back $20k, alluminum around $25k-$30k, and copper can $40k+. Of course these figures are just a generalization. The region you live in will play a large factor in the cost, but these figures will give you an idea of what you will be looking at as far as comparing the different types and materials. Also, keep in mind that there is often an additional charge for tearing off your old roof (usually $1k+) and for any repairs that may be needed for the supporting structure underneath the old roof (this could vary a lot depending on the shape your home is in).
Next you should compare the quality and durabillity of the different materials as well as the cosmetic properties.
Asphalt shingles will last the least amount of time but are generally the cheapest. They tend to dry out with the sun, become brittle, and break apart in the elements. Depending on the area in which you live, this can happen at a much more rapid pace. If you live in Florida a “20 yr.” asphalt shingle may be lucky to survive 8-10yrs but the same house with the same shingle in Montana may very well be conflict free for the full 20yrs+. Asphalt shingles (especially darker colors) also tend to absorb heat, making your attic hotter in the summer,thus, making your A/C work harder and costing more money. A three tab asphalt shingle is the bottom of the barrel when it comes to durability and cosmetic appearance (though, the cosmetic factor is strictly my opinion). An architectual asphalt shingle is generally longer lasting, and thought to be more fashionable than the three tab shingles.
Next are metal roofs. The most common metal roofs are steel, aluminum, and copper. All metal roofing materials will generally last longer than any asphalt shingles. They handle high winds far better than asphalt shingles as well, and often hold up better than any tile roofs in hurricanes. Metal is noted, also, for reflecting heat better than asphalt. Steel is the cheapest metal roofing material, but remember that steel rusts. It will often last as long as aluminum but much more maintainence is required. Aluminum is a good choice considering the small amount of extra cost compared to steel. It also requires little maintainence. Copper is, by far, thought of as a much more prestigious looking roof. It is also much more expensive. There have been reports of copper roofing lasting over 100yrs. with very little maintainence. If you can afford the expense, copper is the most worry free and one of the longest lasting roofs you can put on your home.
Tile roofs are generally thought to be a beautiful choice for a roof. You can expect a long life (often longer than the structure of the home) with any tile roof barring any out of the ordinary circumstances. Tile roofs are fire resistent and require little maintainence. Concrete tile is generally the least expensive tile roof. The benifits of concrete tiles are that they can be formed to give the appearence of wooden shaker shingles among many other things while maintaining the durability of a tile type roof. Concrete tile will (depending on the other added materials) sometimes fade in color and need to be painted over time. Clay tile generally retains is color (though, often limited to few color choices) due to the fact of it being fired into the clay during production. Slate tile is probably the most expensive roofing material you will commonly find. It will often out last the rest of your home, and is frequently thought of to be the most beautiful of all roofing materials. It, too, is virtually maintainence free. It comes in a variety of colors (though, limited to nature) and can be laid in a variety of patterns and styles.
In conclusion, the cost of roofing greatly reflects the duration of which it will last and cosmetics of the product. You must decide what is important to you.
Remember to speak with several roofing companies and request estimates from as many as you can before commiting to one. You will often find one to be far different from another. Also, be sure to ask the amount of experience that each company has at installing the particular type of roof that you desire. You can use the longest lasting materials in the world but if not installed properly, they may not last a year without leaking.