Thicker tips (2mm – 2.5mm) are ideal for the margins. This is mainly because you are usually fishing in shallow water and fish could be bumping into the line so a thicker tip helps you recognise proper bites from liners.
1mm tips are ideal for winter carping where bites can be very subtle. They are also good for silvers with smaller baits.
1.5mm is about right for most carping situations. I prefer a tip about this diametre when fishing pellet / corn etc on the deck in open water. It offers a good balance between visibility and sensativity and wont get pulled under by liners as much as thinner tips.