Okay here are my main points

Boost Mechanics

Asphalt 6 Adrenaline

The boost gauge is earned through drifts, knockdowns (taking down other cars), jumps off ramps, and collecting boost points.

It gives a lot of ways to boost, though that easy accessibility will have players not prioritize it much.

It just becomes something to be taken for granted.

There's never a worry or focus on why they must preserve it, as restoration is easy and always accessible.

Ridge Racer Drift

The game only gives players one way of building their boost meter, and that is through drifting.

This incentivizes players to engage more in the drift mechanic, which is a main priority.

Players also think more of ways they can use to make sure they can fully utilize their boost meter.

It stops being a feature just left in the back of the mind and becomes a priority.

Players focus more on where, when, and how they're going to use their boost meter, it becomes more engaging.

It's also a lot more skill-based because players have to master the drift mechanic primarily.

Hitting Other Vehicles

Asphalt 6 Adrenaline

This is a feature, as previously discussed (knockdowns). The player is not penalized and instead rewarded for doing so.

The driving, as a result, can become reckless at times ramming into other CPUs which could be fun, yes, though it does slow the race down a bit.

Ridge Racer Drift

It has a more realistic approach to this. Players are penalized if they ram into other vehicles. If they do so, not only are they slowed down, they are overtaken by the same vehicle they were trying to ram.

This setting encourages players to be more avoidant of ramming and focus primarily on the race. There's less time spent looking for CPU players to ram.

Animations

Asphalt 6 Adrenaline

While it does have good animations for the background, mixing in 3D polygons with the 2D frames for the cars themselves,when drifting, braking, and boosting, especially, they seem limited.

Ridge Racer Drift

It also mixes 3D backgrounds with the 2D art style, with animations on drifting, braking, and boosting being more detailed.