Challenge and consequences, for one. There are times in TS2 where the words, "Save Early, Save Often" carry so much weight, because some situations or actions carry a chance of real destructive (or at least, inconvenient) consequences of you're unlucky enough. Save before fixing anything with a low Mechanical skill, save before cloudgazing, save before using that telescope...There's tension to the gameplay that just doesn't exist in TS4 at all. There's too much of a safetynet in TS4, too many warnings, chance cards from work carry no risk of demotion or job loss, making money and climbing the ranks in your job are both insanely easy. Nothing keeps you crossing your fingers and hoping you saved before you clicked that thing! They added "Wants and Fears" to TS4, but they lack the real gameplay impact that TS2's had. They're just another useless moodlet generator that don't do anything to increase the challenge, make the game more exciting, or even give you a chance to screw over your sims. With TS4, you can pretty much shut your brain off and not worry about anything. No nail-biting, no save-scumming, no "Crap! When did I last save?!" moments...nothin'.
Next, is freedom of world construction. In TS2, you can totally ignore the pre-built hoods and their pre-made sims and make your own instead! In TS2, one of the best things is starting up a fresh save on an empty hood, building it up house by house, family by family, community lot by community lot, watching the place grow as your story progresses and the plot demands. It's a wonderful unfolding process that really makes the game a joy to play. TS4 doesn't let players do that. The devs control every world: how big it is, what it looks like, how many lots there are, how big they are, what lots are empty ones for the player to build on and what lots go to the devs' sims and buildings, what community lots are where, what types of community lots players can and can't build...it's obnoxious! The one type of community lot they have that doesn't have a stinkin' checklist doesn't even attract NPC sims! And Heavens forbid you put an item that a certain lot isn't tuned to force sims toward on that lot, because ain't no one using it!
That leads me to the third thing TS2 has over TS4: Less intrusive NPC sims. In TS2, I never have to worry about NPC's coming over and pestering my sims on a date or on an outing with their housemates or something. NPC's aren't so addicted to latching onto your sims or any sim within a 100 mile radius that they will barge into your scenes unannounced and start inserting themselves in your business unbidden ceaselessly! TS4 sims are entirely too social, to the point of being downright rude. TS2 sims are much more civilized!