One of the major differences between other forests and tropical rainforests is the sheer amount of biodiversity the latter can have. While upto a dozen plant species can form 90% of a temperate forest, scientists haven't even finished counting the number of plant, tree and animal groups that can be found in a tropical rainforest. Indeed, it has the largest biodiversity of any given biome, which may be why these forests have managed to survive in the form of refugia through several ice ages. Total loss of tropical rainforests would represent a very severe loss of biodiversity.
Thanks to the stable weather and temperature, the species here do not have to adapt to extreme events such as fire, drought, wind gusts or seasonal extremes. They do not need to adapt to uneven hours of sunlight such as the shorter and cold/colder winter days and very long and hot/hotter summer days. There is less climatic 'stress' on the plants and animals here. Temperate regions have stress factors that may encourage monocultures of plants/animals that have adapted to resisting these stresses. Trees/animals here have marked cycles of activity-dormancy. 106
Some may have made clever use of the stress factors to beat competition - eg. candlenuts, eucalypts and certain pines encourage fires as a necessary component of their propagation; grasses have a short lifecycle and disperse light-weight multitudinous seeds to the winds quickly. Tropical plants have no need for these adaptations, the only 2 resources they need to compete for, and they do fiercely, are floor space and sunlight.
It rains fairly evenly throughout the year. The heat and moisture means tropical rainforests have a very quick nutrient cycle and fairly less biomass available freely - things rot away and are recycled fairly quickly. The amount of tree/plant growth possible in tropical environments given adequate sunlight is astounding. Temperate regions do not have this quick cycle. Trees here grow slower.
Tropical rainforests tend to be 'evergreen' - the trees do not all shed their leaves completely at any given time, the forest does not turn bare, as in, say a temperate forest. The very large swathes of 'green' photosynthetic area play a very important role in maintaining the climatic conditions of the area throughout the year. This further damps down marked seasonal swings to some extent.
You may be very interested in reading what this article has to say: http://www.rainforestconservation.org/rainforest-primer/2-biodiversity/d-why-is-there-so-much-biodiversity-in-tropical-rainforests/
Some resources comparing tropical and temperate rainforests: http://quest.arc.nasa.gov/projects/jason/xv/docs/TempRain.pdf http://w3.marietta.edu/~biol/biomes/temprain.htm 1022