They are both Islay's, where the peat comes from....But Lagavulin is the top dog when it comes to the Islay's and the difference between the two would be like rubbing alcohol vs Grey Goose (IMO). Laphroig gets good praise, but I think it's shit compared to Lagavulin 16. I do like the peat though. Got a bottle of Ardbeg too (another Islay) and again it's no comparison. Been trying to find something I like as much as the Lag but cheaper, so far I have failed.
Lagavulin in a neat situation is ok in my book.