Which field is better Information Technology or Software Engineering?Does degree from a good institute matter?

Agreed with Usama Hafeez, Software Engineering is more into programming and IT (Information Technology) is refer to generic IT field.
Both have good future, so do not need to worry about future, if you have a good knowledge and (die hard) interest in Computer than go for Software Engineering and be a superior Software Engineer.
Ah but if you don't have a good start with Computer as field than you must join IT.
(My thinkings, as a Software Engineer Student)
Don't spoil yourself into unknown field, instead be a professional with closely known skills

Yes the degree does matter, and the software engineering is much better field for you and it's in demand now a days, uptill next 15 years in every country.

Well, you have to see the courses for both the degrees. IT sounds more generic while Software Engineering is more into programming, its management, testing etc.

The most important question is, which field excites you. If you're not passionate about the field, its probably worth finding something else. A huge number of students get into the computer science side and in their very first year start questioning what they're doing. But if want this field, then great go for it! I had a passion for programming so I did software engineering. It has a combination of hands on courses and other dry theory courses. So make sure you see what courses the degree is offering.

Yes, the institute matters not for the degree its offering (well actually it does for that too if you want to get a job based on the "name" of the university). Mainly you want to see what the students say about the institute. You want to see how the professors teach. Do they go on with boring slides and make you memorize texts or is there a hands on approach. MIT has many of their courses on video available for free online. Search for that. I would say an institute that comes closes to this teaching methodology is the one you're looking for

Software engineering is better field for you.
http://www.jobz.pk/engineering-jobs/