These days I do mostly adventure and monster design. I don't actually enjoy full system design as much as I enjoy doing new and interesting things with established designs -- probably because I do not have the sort of personality that does well with carefully testing and iterative development (which I think are key to good game design).
Anyway:
Monsters: whatever form it takes in whatever system I am designing for, the key for monster design is for the monster to be easy to run for the GM, and provide for interesting and fun gameplay for both the GM and the players. A lot of times that latter part means giving monsters more to do than simple attacks, and things to do in response to player actions (reactions, if talking about 5E or related games). Even easily defeated minion type monsters should be fun to run and fight against. I really like the monster attack tables from Dragonbane and want to incorporate something like those into some professional work for other games.
Adventures: I am a strong believer that it is essentially impossible to design an adventure for any given table of players that isn't yours, so in adventure design I think the best bet is to give the GM tools to work with to run the game for their players in the way they run games. The Savage Worlds "plot point campaign" (PPC) is a good example of this in general, although my inclination is to give GM more tools than is typical for a PPC. I hate it when designers bury important information in walls of prose, and I think one-look maps and actually useful relationship mapping and event flowcharts are essential.