just read up on mlb 2006 and it sounds like their career mode is similar to pawapuro's 'my life' mode (which means i may have to check it out this year). 'my life' is an rpg-like mode where you make your player and take him from the 2nd team (i.e. minor leagues) and try to work your way into the big leagues. you improve your stats by playing and training. games are really short if you're a batter since you only take your at-bats...and pitcher's only play when they come in for a relief appearance or start once every 5th day.
there's meters for your player's releationships (with agent, coaches, teammates, various players on opposing teams, and female fans)...i'm not sure exactly how the relationships affect your on-field performance though since i'm not literate in japanese.

i do know that in previous versions of the game, you could eventually marry and have kids but i've been unable to do that in pawapuro 11.
there's also off the field activities that you can do (extra training that improves stats or various recreational activities that can affect your mood) and items you can buy. items can increase your off the field options (i.e. golf clubs, remote control car, gaming console) or restore stamina (which is lost whenever you play in a game as well as when your team travels). most of these things are menu driven, so it's not the most dynamic of systems but it's nice to be able to manage your off the field life.
and since this is turning into a long post, i'll just quickly add that you also have a salary complete with post season negotiations, a popularity meter (being real popular helps all-star voting but can drain you even more when you travel...since you'll occasionally get mobbed by fans and lose more stamina than you normally would when travelling), and a trophy case that houses balls/bats/awards from any significant career achievements (1st hit, 100th HR, player of the month awards).
er, yeah...so that's 'my life' mode in a very big nutshell. i love it (even if i can't understand everything right away) and hopefully more devs will incorporate it (particularly the off the field stuff) into their sports games.