Which is better, NIT Trichy (EEE), NIT Surathkal (ECE), or IIIT Allahabad (CSE)?

All the three colleges mentioned by you are quite reputable. As for rankings, they keep changing with time. So you should focus more on the branch that you’ll be getting at each.

ECE contains subjects like Semiconductors, Digital Signal Processing, Microprocessors, etc. These are quite difficult. As per the present trend, mostly IT companies visit the campus for placements. Though ECE students are eligible for almost all IT companies, you’ll be asked questions on Java, DBMS, SQL, Data Structures, etc. All these topics are included in the curriculum of CSE/IT.

EEE and ECE students go through difficult subjects. However during placements, except a handful of core companies, most of the job offers are made by software firms. As a CSE/IT student, your studies will come handy during placement rounds. Only a handful of core companies like Texas Instruments, Brahmos, etc. offer jobs to Electronics engineers. 

For placements in Google, Amazon, etc. at handsome salaries, I would recommend you choose the CSE branch at IIIT Allahabad. Instead of going for the top IITs/ NITs, choose your college according to branch.