Mechanical engineering obviously covers alt. energy.. I don't understand the point of this discussion while all manufacturing processes in the preparation of the structures needed, the design process of solar energy towers, blades of wind turbines, towers of wind turbines, cooling towers of nuclear, geothermal, and hydrogen plants, turbines of hydro-electrical plants are covered by the mechanical engineering degree in form of manufacturing processes, advanced manufacturing and control systems, micro-mechanics, thermodynamics, fluid mechanics, materials and statics-dynamics units...
The only stuff the EEE would do in the field of alternative energy is to design an electrical motor, and maybe the circuits involved, and of course the power storage systems to tackle the problem of unpredictability in most alt. energies.. In mere technical terms the mechanical engineer is responsible of the process of creation of motion, and the electrical engineer is responsible of turning it into power by the simple magnetic engine and storing it somewhere.
You should grow up and realise that mechanical engineering is not simply about cars and petrol engines.. In fact that is just a light-small module you opt for in the last year and that no one actually cares.
The ones saying EEE is a low paying job are also wrong because of the high demand in the IT industry, Mechanical engineers earn just a little bit less because the field ME s work in is much more broader and the wages vary a lot (regarding to the school you've graduated, the sector you are working in), say a ME working in field of a small aerospace company would earn less than a ME who's in management of a big multi-national (and the best thing is that this depends mostly on your ambitions and preferences, and on your luck as in everything). If you are in engineering just for the money and not for curiosity go for Petroleum engineering, you'll earn a lot but you might end up in a lost platform in the middle of the ocean. Electrical engineering is a respectable degree, and is also a hard one to finish, as it is the case in Mechanical engineering. ME is obviously much broader and is less affected by a recession in a single industry, but this doesn't make one superior to another, that is out of question cuz they are different fields...
Mech. eng or EEE is just a question of preference.. If you are god with HS dynamics and thermodynamics go for ME, but if you are good with HS electricity ( mostly on AC) in physics go for EEE. Obviously you need a strong mathematical background but that is true for any engineering degree.
Wish you good luck in whatever career you choose..