Asphalt shingles are easy to replace, but they wear out quickly and can be damaged by strong weather. The problem with all kinds of shingles, both wood and asphalt, is that weathering slowly deteriorates them. Asphalt shingles shrink and wood shingles rot, the eventual end result of which is water damage through the roof below. Wood shingles have a long history in Europe but have been replaced by asphalt and other synthetic materials in the US for most common applications.
On the other hand, the low cost and flexibility of shingles make them more resistant to impact than tile, and the replacement cost is lower. Tiles are also more fragile when it comes to people walking around on them. Tile can break and fall off, causing a hazard. The tiles may offer more protection from impacts, at the expense of destroying themselves. Roof tile is made from a hard material like ceramic, clay or slate. There are many different styles, from Spanish rounded roof tile to simple square slate tiles. Tile is heavier than shingles, so when switching roof styles, hire an engineer or Denver roofer to check your roof for structural stability.
When it comes to insulating abilities, roof tiles work a little better than shingles because they are made of thicker material. The real difference in heat loss is your insulation in the attic. Proper insulation and venting will make much more of an impact than the type of Denver roof materials you choose.
From a pure aesthetics standpoint, only wood shingles can compete with tile. Tile looks cleaner and more masculine because of its thicker shape. The barrel roof tiles of southwest architecture are usually red or earth tones and give a more laid back tropical image.
If you want to really go crazy with your roof, hire a custom roofer that knows how to do old-school European shingles. There are many designs to choose from and your roof will definitely be unique.