I'd propose looking at your question from the perspective of your potential readers. I'm also using an information security viewpoint here: in security there's a concept of the CIA Triad, that is, the Confidentiality, Integrity and Availability of your data.
Since you are sharing your paper publicly, Confidentiality is unimportant.
As a reader, how do I verify the Integrity of a paper I find online? If it's on a university's website and I can follow breadcrumbs to it from the official, current faculty listings to the author's homepage on their university (
.edu) website, I can be reasonably confident that it was posted by the actual author. If the paper was posted at ProfessorSmith.com I have less confidence, unless perhaps I've met the author in person and they told me that's their website and they're still paying the hosting bills. If the paper is posted to a free site like johnsmith.freewebhosting.com and there are lots of spelling errors I might suspect someone else is masquerading as the author.
Integrity isn't just the source, though: whether or not the paper was posted by the real author, there's still the question of whether the paper has changed from the published version. Maybe the author only fixed a typo or cleaned up a graph that had rendered poorly in the published paper; maybe they accidentally posted an older pre-review version of the paper; maybe they were upset about a change that a reviewer had demanded and reverted the change before posting it on their website; maybe someone deliberately changed some data to throw off other researchers. The only way to truly verify the integrity is to also get the paper from the journal and closely compare them: in which case there's no reason to get the paper from the author's website in the first place!
What's the long-term Availability of your paper? If you put it on a self-hosted web site, will the paper disappear when you stop paying the hosting bills (whether you forgot, have something better to buy or just aren't around any longer)? Could you accidentally delete the paper when you update your site, or make some other change that makes the paper inaccessible? If it's on your home page at your university, will it disappear when you leave your position and your account is closed?
Now that's not to say that you shouldn't post your papers on your personal website! There are plenty of other, casual uses for that (the paper could get indexed by a search engine and someone will find it in a search and lead them in the right direction; someone mildly curious in the topic will have a better chance to find and read it; someone with limited funds can see if the paper is relevant before forking out for the official version). But for someone who needs your paper (or at least its conclusions or methodology) for their own work, the best source is the original journal which in most cases will provide better integrity and accessibility than your own site.