Hello Aspirant,
Here is the comparison between ECE and ME.
In case of opportunities in both of the Govt and private sector, i would like to take the side of ECE. If you want to walk with the trend of current market of our country, then you must choose ECE.

Other than this point ,mechanical engg is an evergreen engineering field. This field has very good prospectus in the Govt and as well as in the private giant construction sector.

As an electronics engineer you can indulge into both your core field and as well as in the software field if you want.

Major software MNCs have requirements of engineers of ECE background also.
GOOD LUCK!!