It depends entirely on what you want to do, the first question is, do you really need to pursue a degree?
First off. Let me clarify a misconception you seem to have, you already have a bachelors degree, so you can apply to masters programs. I see a lot of people make this mistake, you don't need to have a bachelors in a field to pursue a masters/phd in it, so yes, you'd get a masters, a bachelors would be a total waste of your time.
The fact is that the vast majority of what you'll learn in school in either program will have little to no relevance to what you'll end up doing professionally. The majority of your day to day work will involve self taught knowledge bout frameworks, languages, etc. Technology advances at too fast a pace for a university setting to remain up to date.
So you have a choice, self study and practice for 6 months to a year, contribute to some open source projects or make your own, and then try to look for work, or...
Go to school for several years and then seek employment.
Which is better depends on your goals. Education is nice because even if you decide you hate this field too, having a masters in anything will make you more valuable as an employee, so you'll earn more on average even in a different field.
The downside is time and potential cost(though most grad programs don't end up costing anything, it's a pretty big loss in terms of opportunity costs).
As weird as this is to say, if you think you'll be a mediocre engineer education is the better route(they'll weigh your credentials more than your performance), however if you're legitimately good at it, practice and you'll have no shortage of high paid work regardless.
Now, as for CS vs SE.
I'm a computer science educator, and let me be clear about this, I've said this several times in the past:
The purpose of computer science programs is not to teach people how to build software
They do not pretend they are, mostly do not claim they are, and in no realm of the imagination will they teach you those skills. It is not even slightly uncommon to be like me, PHD educated in this field, and I didn't really have a clue how to build practical software. It's a skill I've had to teach myself entirely.
CS programs primary goal is to train academics and researchers, followed by system architects. Not "programmers".
A software engineering program is probably more what you're looking for, but they will still likely focus more on system architecture than on practical real world programming.