I've gone from DMing AD&D 1E games for friends to my kids to paying clients as a team building tool. I've seen the approaches of playing a character as an avatar of myself and playing a character as a chess piece in depth.
Personally, I prefer playing as a chess piece myself. I find it more challenging and more fun. I know that many, if not most, people prefer playing as an avatar. This seems especially more prevalent when starting out as a new player.
Just from observation, I notice that most players, playing for fun, play as an avatar in a sandbox game that allows for more free choice and movement. Sandboxes are a very player centered game environment. Specific adventures seem to allow for more exploration of the "chess piece" player approach because it gives the player the opportunity to focus on achieving specific goals and objectives both individually and as a group.
My team building games are always run as specific adventure, avatar played games. These folks are paying for more than a fun, "get away" game. This is as much training and education as it is (hopefully) exciting.
I always have clients start with character creation because it gives them the opportunity to build their back story and build something of themselves personally into the player character.
There is usually a brief sandbox session right off to allow the players to explore their capabilities and the game world parameters they must operate in. Then the specific adventure session follows. I custom write a session for each client group to meet the skill building objectives they want to focus on.
I've had players in client groups try to play chess piece style while the others play avatar style and if anyone walks away from the experience saying they didn't get much out of the experience, it is those players. Avatar style playing allows for more personal investment in the player character and the game. Not making that investment, the player takes little away from it as well. It truly is a "you get out of it what you put into it" situation.
I will take client groups of people in management positions into games in "chess piece" mode. This serves their training purposes better. Their goals are usually focused on resource allocation and management. "Chess piece" style is very appropriate to that objective. This as well as group strategizing, goal setting and setting group S.O.P.
I do very little gaming outside of client based games anymore. If I do, I'd like to do so as a player. Not an easy task for me in my area. Like I said earlier, my preferred personal playing style is is "chess piece". I like to take my own created characters and explore the potentialities to their extremes.
However, I get just as much fun taking a random pre-gen and just making the most of it. Winning is important in my gaming. Overcoming obstacles, being the first or best or having the highest score is the whole point of playing any game for me.
Which style do I find myself winning with more often? To be honest, I'd say in avatar style. Perhaps that's a bit of an easy win for me though with my having so much experience and familiarity with the game as a DM. However, in "chess piece" style, I can focus more on learning and experimenting with abilities and skills relating to class or race capabilities. In the long run, I improve over time at playing a given class, race, etc... regardless of dice determined abilities and increase my opportunities to win no matter the character type.
No matter what your preferred style is, you should be having fun. Otherwise you're doing it wrong.