Way more dynamic objects (vehicles, destructible environments) with a much larger playable area (more room for more objects). Usually objects further from the player are updated less frequently (to deal with the sheer volume of objects) but may still be visible to the player, client-side prediction comes in handy here.
Also the need for more detailed positional/vector data for much more complex physics simulation, which also requires both a higher resolution of updates to function realistically. Additionally, fast moving vehicles with more delicate control/handling, such as fighter aircraft, also a require higher resolution of updates so that you can actually fly them without crashing due to the feedback loop of perceiving jerky/delayed movement and input response. Prediction can help to smooth this out.
Additionally modern games use things like physically simulated projectiles (think bullet drop[1]) with collisions calculated using mesh-based collisions instead of simple hitboxes, over much longer distances, so there is a need for prediction as timing is more of a factor. Quake 1, 2 and 3[2] use the 'hitscan' method[3] of calculating whether a bullet hits its target, which is instant and calculates a linear trajectory, which has the side effect of making it easier for players to adjust to lag (basically any difference between the player firing and the hit registering is network lag, and should be more or less consistent).
Finally, two slightly different issues that have become apparent in recent years are automatic match-making and local servers (ie, the game running on one player's console). Auto matchmaking is often fairly shitty, meaning that (on average) players end up playing on servers to which they have a higher ping time than if they had chosen the server from a server browser (something that is sadly becoming rare in today's games). The phenomena of local servers, on the other hand, puts pressure on the total available throughput, rather than ping time, as the player that is hosting likely has more limited outgoing bandwidth than a dedicated server might.
[1]http://en.wikipedia.org/wiki/External_ballistics#Bullet_drop
[2] only for some weapons, a rare exception for the time
[3]http://en.wikipedia.org/wiki/Hitscan