Hi
EE is surely more popular than mechanical these days . Electrical engineers are in demand these days and are offered decent jobs . Electronics has taken a place ahead of electrical .
A number of scientific and technological advances have taken place in the field of electrical and electronic engineering, which is why it offers immense career opportunities. There are many job openings for graduates in this field. You can find employment with the government as well as companies engaged in the manufacture of consumer electronics, electronic components, computer hardware, radar, medical equipment, automation and control systems, private utility companies and companies manufacturing electrical appliances and instruments. 
Mechanical engg. is good but it does not offer much high paid jobs and also electrical engg. opens ur scope for software firms too as programming is one the core courses for ee . Moreover , Girls do prefer electricals much more than Mechanical , this is what the trend is , although there's no problem for Girls in either of the streams.
So, my suggestion would be Electricals.