Welcome! Here are the website rules, as well as some tips for using this forum.
Oil Burner Comparison & Differences
Beckett and Carlin are similar burners-some prefer 1 over the other-one may work better in a particular boiler than the other and they use some of the same parts.
Riello is a little different burner-no doubt about it's quality-works great in some applications-has different pumps and different parts-probably more proprietary parts than the other two.