It's not the same thing at all. Obama didn't block people who already have valid visas. Obama didn't block green card holders.
Why do you say it's the same? Do you consider those two things to be essentially the same, or are you ignorant of the actual substance of one or both of these actions, or what?
This policy is still not the same though, no.
The previous administration only suspended Iraqi refugee processing for ~6 months.
The thing I'm mostly annoyed about is people claiming "only the new administration would pick this list of countries" when they inherited the list. I'd much rather we focused on how much worse things they're doing with the list instead.
I totally agree that focusing on the list itself is silly. It's a good example of why Trump should have divested his business interests prior to taking office, to avoid this kind of questioning of his motives. But it certainly doesn't look like these countries were chosen in any way based on his business holdings.