Self Levelling Compounds are intended to level (plane) large and small floor areas. It is very expensive and would be a waste of money in this case when you can do the same thing with a bag of sand mix or mortar mix. Generally speaking a 50# bag of self leveller will cover 50 square feet 1/8" thick at a cost of about thirty dollars per bag. Sand mix - 5 bucks.
Self leveller also has limits as to how thick you can pour it at one time. You can add pea gravel to bulk it up but there again, why go through all that?
How deep is this depression anyway?
As far as the epoxy goes.....NOTHING will bridge the gap permanently, not even epoxy. I'm imagining the information you are getting about the benefits of the epoxy is coming from people that sell epoxy. Use a crack filler and keep your money in your pocket. There are also concrete-patch type caulks available for filling cracks. These crack fillers come in a tube for dispensing with a caulk gun or you can buy them in "pourable" form that will self level.
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