A concept from Persona 3 that has been noticeably improved in Persona 4 is the set of attributes that represent the main character's strength of personality and ability to interact with other people. These attributes don't factor into combat at all, but they can have a significant role in the hero's day to day life. In both games, you improve these attributes by spending time performing certain activities,This is one of those elements that I didn't really like in Persona 3, but the changes made to the concept in Persona 4 have made me warm up to it. I may as well just go over each change one at a time.
1) The number of attributes has increased from three to five. Persona 3 had just three attributes (Academics, Courage, and Charm), but Persona 4 has five (Academics, Courage, Diligence, Expression, and Understanding). Charm was my least favorite of the original set of three, since the attribute it was supposed to describe (how popular the main hero is) was built up in the least logical ways (answering questions in class and drinking coffee?) and didn't make a lot of sense because of the Social Link system (why is popularity separate from the main measure of how many friends you had and how much they liked you?). However, it was removed, and has been replaced by three other attributes that make a lot more sense. Like Knowledge and Courage, these new attributes describe the hero's capability to do something, rather than the extent to which he has done something like Charm did, which better matches the actual function of these attributes. Also, the increase in the number of attributes greatly made it necessary for the game designers to increase the variety of activities you need to do in order to raise the hero's attributes, which adds to the variety of the game a bit. What is more, the added number adds to the difficulty of building them up, which forces the player to specialize a bit and adds to tough and interesting choices in daily activities.
2) Attributes have more uses now. In Persona 3, the hero's attributes only affected his grades on tests and limited your ability to unlock a small number of Social Links, but in Persona 4 they have many more uses, and these uses are more dependent upon individual attributes. Beyond just unlocking Social Links, high attributes are required to progress through some Social Links or get hired for part-time jobs. A number of conversation choices throughout the game require higher levels of certain attributes, particularly Courage and Understanding. Raising some attributes increases how much you get paid for part-time work. Raising Diligence lets you go fishing for longer periods of time. These changes make improving attributes worthwhile across the entire length of the game, so there is no longer a clear point where they start or stop being useful.
3) There are more ways to improve attributes now. In Persona 3, you primarily improved your attributes by going to class, going to restaurants or entertainment venues, and studying. There were a few fun alternatives, such as donating to the temple (in the original version only) or visiting the Nurse's Office while sick, but mostly it involved going to a restaurant and wondering why eating tuna improved your Knowledge. Persona 4 makes some much-needed improvements, so now it is much easier to raise attributes in a variety of ways. You can raise some attributes by going to club meetings and working at a part-time job (so it is now possible to strengthen Social Links and improve attributes at the same time), Courage can be raised by defeating powerful enemies, Understanding can be improved by choosing certain conversation options in plot events, and many attributes can be built up simply by reading a book (so buying books and obtaining rare books through quests and events adds some new versatility to the system). As a whole, you will see improvements to attributes far more often in the new system, and you don't have to make a choice between improving attributes and building up Social Links anywhere near as often, which is good because that choice is inherently one-sided in favor of Social Links.
All combined, attributes are simply more important to the game now, and add a lot more to the game experience. Of course, the system is far from perfect, but I am nowhere near as critical of it as I used to be. If the next Persona game simply takes the changes made in Persona 4 a step or two farther, it would probably improve the experience even more. For example, I certainly wouldn't mind seeing these attributes affect the dungeon exploration side of the game, or vice versa.