Random advice from the interent:
+ The important part of blogging is blogging, not selecting a platform. It is more likely that a blog will die because it is not written for than because there is an issue with the platform.
+ Completing a graduate degree is likely to open more doors than a blog. Partially because that is just the way the world works. Partially because most blogs contain statements that are either outright errors or easily misunderstood so as to be an error. And people deliberately read blogs to find errors and are predisposed to misunderstanding blogs as containing errors. That's just the way the internet works.
+ Linkedin is useful for maintaining loose social/professional connections. Which is to say it is good for keeping up with your current and former classmates and coworkers. It is ok for research on individuals at companies where you want to work, but as a general rule it is a mediocre way to reach out on a personal level -- it achieves mediocrity because it is easy to use but that ease of use means recipients place a low value on communications within Linkedin.
+ A job will be more valuable in terms of future jobs than a portfolio project. In part because it will be validation in the world of work rather than academia. In part (and this is where Linkedin comes in) because it will expand your professional network to include the coworkers.
I am not saying not to do a portfolio project. But slacking off on a degree in order to do one is not going to improve most people's attractiveness as a job candidate. On Linkedin the degree will still be on your profile five years from now. If a student project is there five years from now, that's probably not a good thing.
In the end, Linkedin can supplement import relationships and achievements in the real world. It cannot replace them.
Good luck.