Have done this numerous times myself, so here are my thoughts:
Check everyone is going to be happy with the new campaign.
This first one is hopefully obvious - ensure everyone is happy with the choice of new system and genre, and indeed with the fact there's going to be a change. Sometimes that character investment will leave them wanting to hang onto the old setting just to continue the story with new characters and occasionally run into reminders of things their old characters did.
Apply the same personal touches that worked last time
Try to remember some of the personal GM touches you brought to the game that made it enjoyable. For example, if they liked particular types of NPC characterization, or the injection of odd humorous moments. Try and fit those into the new campaign. Maybe even put in some NPCs based (as loosely or tightly as you feel is appropriate) on their favorites from the old campaign.
Don't allow the new system and genre to force unwanted changes.
Similarly, ensure the new game doesn't prevent players from having the same chance to inject their own personal touches. If it's usually, for example, an overly-serious setting and you know your players are very humor-orientated (or vice versa), don't force them into a purely serious storyline.
Remember that table preference can trump both genre and system leanings if you want it to. A system-heavy game can be stripped down to basics if that's what your players prefer (yes, those hundreds of pages of Pathfinder really can be summed up as "roll a d20 to make a check against a skill or attribute, we'll figure out the rest as needed" if you really want to make it that simple), and a system-light one can always be beefed up with house rules - you can always add in critical hit tables, skills and subskills, and class-specific abilities for games that don't have them. If everyone enjoyed playing a game that made heavy use of cards, consider creating a system for using some in the new campaign too (hint: DriveThruStuff have a print-on-demand system for cards.)
Different, but still the same
And now a tip on the player side: If they're overly attached to their character, it can help to imagine an actor that was playing their character moving on to play their new character, in the same way some people can enjoy watching the same actor in different TV shows.
For some players, they can't imagine the actor as anyone but themselves, but for others they have a particular physical and psychological feel for the character that's different to their own, and carrying that over to their new character can help if they're feeling too detached in the new game.
Other players may of course relish the idea of throwing out the old and starting anew, and this is the perfect opportunity to do so. Try to ensure anyone that's bored with their old party role gets to try something completely different.
