What does the player have access to, full stats of the cohort, or something less?
The players usually make the cohort and completely control them (in and out of combat). That is for PC made cohorts. For NPCs in the game that players through role-playing managed to pick up with the leadership feat, the player still control them, but the DM has veto power on the cohorts actions.
What about character creation for the cohort? Do you use the same rules as PC creation, or something else? Who creates the cohort, DM, player, or a joint effort?
Same rules as PC's for PC made cohorts. NPC cohorts that the players have picked up through role playing are usually a little better or more unique.
How much control does the player have over the cohort, and when? From what I hear, many games just allow the player full control over the cohort, like a second player character. We will almost certainly go with something less than this, but the question is how much less.
see above. Usually full control.
How are XP and treasure rewards handled/divided (especially if other than per the DMG)? Are the new XP rules for cohorts working out, or are you using something else?
We use a different system. When the PC levels, he levels the cohort as well. Also the cohort must always be at least one level behind the PC. As far as treasure is concerned, it is up to the PC to give the cohort treasure. Sometimes, they get items the party deems it is necessary or helpful for them to have.
Especially concerning treasure, it seems like other players may get the feeling the the presence of a cohort takes away some of the party's treasure, almost like the player with the cohort is double-dipping. Any problems in this area?
see above.
What works and what doesn't -- DMing technique stuff, rather than rules judgments. What do you like about the system you use, and how would you change it?
We don't like to have all 5 players at the table have cohorts because it really bogs down combat, especially after 16th level. For the most part people pick up cohorts for roleplaying reasons or to vill a void in the party (lack of a rogue for instance), so we like the system.