While I was searching for a listing of aircraft with different anti-/de-icing methods - especially for electro-thermal wing anti-ice - I couldn't find any information about other aircraft except the B787. Is there any reason, why other methods like TKS or using bleed air were prefered in the past? Are there any studies related to the pro's and con's of the different anti-/de-icing systems?
Partially because 787 has no bleed air available for any purpose. Its engines do not draw bleed air traditionally. Any pneumatic system draws air from other pumps. Hence electro-thermal wing anti-ice system is needed since no bleed air is available.
Traditional anti-ice systems use engine bleed air through the pneumatic system. Engine bleed air is air that is compressed by the engine compressor to high pressure. Due to thermodynamic effects the air also warms to fairly high temperatures. This air is then bled off the engine through valves to supply the aircraft's pneumatic system. The pneumatic air is then sprayed on the inside of the leading edge of the wing or engine cowl to prevent ice accumulation.
Engine bled is a very expensive source of energy on an aircraft because compressing air isn't that efficient, the engine core has to be slightly larger to accommodate the increased airflow, and the pneumatic system itself is typically one of the least reliable systems on the aircraft. The system also uses many large ducts that are heavy and take up a lot of space, which dictates larger passages in structure, which is more weight again. However, bleed air is available making it an attractive source of energy.
The 787, however, shed the vast majority of the pneumatic system (see the link Sports Racer posted above http://www.boeing.com/commercial/aeromagazine/articles/qtr_4_06/article_04_3.html). This decreases the specific fuel consumption of the engines quite a bit. Reduces weight, and removes an very unreliable system from the aircraft.
The 787 is able to get away with this because it has very advanced electrical starter/generators. The generators can produce about 500 KW each, significantly more than any other Boeing aircraft. Since there is so much power available, electronic heater blankets for anti-ice are feasible, no other Boeing aircraft has the excess power to use electric anti-ice on the wings. Besides being much lighter, the electric blankets will use the energy more efficiently as well.
Although the generators still pull power off the engines, increasing fuel burn, the process is much more efficient than using bleed air.
FYI: The generators are also the engine starters, which eliminates another major pneumatic component on other aircraft.