This came up on another Post I had started about What needs a second play in your collection. Some games seemed to be designed with depth in mind that needs many plays to really mine those depths. The pros are tons of replay-ability and satisfying game play. However, the cons is that you need to have time and a group who will play the game over and over to get to those depths. Many times, these games seem to not be the ones that are "love at first play" (unless these are the style of game you are into).
There also seem to be a group of games that are designed to be engaging from the start, are easy to learn and teach and fun to plays. All pros to this style. They seemed to be designed for the gamer who plays a game once or twice and is on to the next hot game. But the cons are that they seem to "fall flat" after multiple plays and they either aren't as satisfying or are easily "solved".
Obviously these aren't the only two ways that games are designed and there can be a game that has mix of both. Also the same game might have lots of replay-ability with one game group and feel flat to another so there is some subjective personal preference here.
So all that being said, do you find that you gravitate toward one or the other in your collection? Both? Do you look for one kind of game or another when you're deciding which ones to buy?