They're slightly different to one another.
Sof סוף is a noun meaning "end", and doubling it up makes it an adverb, "finally". To emphasise it, you can say סוף כל סוף, "at long last", "finally".
Le'at לאט is already an adverb, but doubling it up is quite common, and probably more common than just saying it once. I can't say why this is.