This is written by me but the info and experiences are from the HP2010 community over the years, I’m not nearly as fast as the best of them and just concluding some of the key points. Feel free to try out yourself, maybe there is something that isn’t covered or isn’t completely correct.

The most characteristic and vital part of the handling system, this BTD seems mostly like an improved version from Burnout Paradise and also looks similar to Ridge Racer series. However HP2010 emphasizes feelings of weight of the cars, and initial turn-in is quite slower. Anticipating when to initiate the drift is the key to control your racing line.

And there is the rubberband model of drift speed. The larger your angle is, the lower your speed will be. Different cars have different drift angle for the same actual steer angle and different cornering speed. If you can complete a drift without touching your tail to anything else (that will immediately cancel your drift), when you are nearly ending the drift you will be doing 90%-95% of your entering speed, or ~20-30kph lower. The rubberband effect when you reduce your drift angle will cause your car to accelerate rapidly, perhaps even faster than cop nitrous. Which means your speed largely depends on how long you can maintain your drift out of a corner, and the power of your nitrous.

Note: Rubberband really is only a way to describe how the car slows down when increasing drift angle and 'bounce back' to near entry speed when you decrease the drift angle. This differs greatly from Ridge Racer in which drifting is almost frictionless. In certain cars it is possible to countersteer without ending drift too early to release this explosion in speed, but it requires tailored, model-specific muscle memory.

Release and Press Throttle key again on keyboard, or lightly press brake trigger on gamepad to minimize speed loss to initiate a drift. Consider a pull of handbrake in a drift when facing tight corners.

Skilled drivers will time and use up their nitrous right before starting a drift to maximize cornering speed.

Crashing sideways into traffic/road block while drifting will not affect your speed very much, as it will recover in a magic fashion. Exploit it to your advantage.

All nitrous seem to be constant in acceleration instead of power (in physical sense), thus it is best to use them at mid to high speeds.

Nitrous is gained by: drifting (regardless of angle, favoring small-angle drifts), Racer driving oncoming, near misses (oncoming near misses don’t count for cops), and taking shortcut. The gaining rate seems to be constant across all cars, and the backmarkers will have increased gain rate.

All police cars share the same nitrous, which is very powerful but used up quickly, and cannot reach top speed. However they are also free from many behaviours in Racer variant.

Racer nitrous differentiates from car to car in power, and also in depleting rate. It can reach the same top speed as Turbo if used long enough, but:
a) takes a second or so to reach full power. (Avoid spamming nitrous button.)
b) is wasted in the intervals of gear changing. (Thus generally cars with less number of gears will perform better under nitrous!)
and c) may push the revs higher than usual at the same speed, causing earlier upshifts. (It is impossible IRL but this game’s rev counter does NOT correspond to actual engine speed.)

c) becomes a problem because the overdrive gears many cars have. These extra gears make sure that every car of the same tier will have comparable top speeds under nitrous/Turbo (280/310/350/380/410 for T1-5 respectively). However many of these extra gears will make the cars slowing, and cannot downshift until below the redline. T4 Murcielago/Reventons and 911 GT3 RS are some examples that suffer greatly from this.

Because backmarkers only get a gaining rate boost to catch up, it is advised to pick a car with strong nitrous in case you f*cked up in online lobbies. The best TA cars of each class are all equipped with the best or at least above-average nitrous.

Mostly the choices for WR attempts IIRC. Some cars in Cop can be much faster than Racer variant due to improved nitrous and top speeds, and the cars with very high top speeds in Racer will be nerfed in Cop.

Tier 1: Mazda RX8, Porsche 911 Turbo
RX8 has decent top speed and a seamless drifting handling, even capable of straight-line drifting, but turn-in is slightly slower. 911 Turbo has great nitrous, only 5 gears and highest top speed in class, but its drifting is trickier.
Avoid Evo X.

Tier 2: Maserati GranTurismo S/GranCabrio, Carbon E7 (Cop exclusive/removed in Remastered)
This class is perhaps the most balanced one, the Maseratis are not vastly quicker than anything else. Carbon E7 has very high top speed even among the cop cars.
Avoid Challenger, 8C Competizione hardtop.

Tier 3: Mercedes-Benz SL65 AMG Black Series, Aston Martin V12 Vantage/Porsche 911 Speedster (only in events w/ highway/many long straights)
In capable hands, SL65 can do times that can rival the best of T4 cars. V12 Vantage and 911 Speedster have absurdly high top speeds under nitrous/Turbo (380+kph), can even beat SL65 in straight lines.
Avoid Panamera.

Tier 4: Dodge Viper SRT-10 ACR, Mercedes-Benz SLR 722 Stirling Moss (removed in Remastered)/Lamborghini Diablo SV
ACR has the best cornering speed in the class. It has overdrive gears but downshift point is at ~335kph so the loss can be mitigated. Stirling Moss/Diablo SV are better at high speeds.
Porsche Carrera GT, Pagani Zonda Cinque are much better in Cop for enhanced top speed and nitrous.
Avoid Ford GT.

Tier 5: McLaren F1/Gumpert Apollo S, Koenigsegg CCX
Both F1 and Apollo S have great cornering capabilities and rocket nitrous. I’m not good enough to determine which is faster though.
CCX can retain its speed at 400-410, makes it faster on long straights, and the fastest for Seacrest Tour.
Koenigsegg CCXR Edition, all versions of Veyrons have very poor nitrous in Racer. They can be actually relevant in cop versions.
Avoid Agera.

Because many people have asked about this, I have done some experiments regarding to car weights. It is not conclusive, and may be changed later on.

The weight does not affect the health bar, a heavier car will not sustain more hits before it goes down. However, basic collision physics is still respected, that means a heavier car will have a larger momentum and affect the collided's speed more than a lighter one. If you are in a Racer McLaren F1 (1138kg IRL) and a Cop Veyron (1838-1990kg IRL) is catching your tail, without any countermeasures... good luck.

Obviously you can search wiki to find out what exactly the weights are, but generally muscle cars (not American sports car like Corvette/Viper/Ford GT), grand tourers and sedans are the heavier ones in their class, and exotic supercars and trackday specials (e.g. Sesto Elemento/Zonda Cinques/GT3 RS) are the lighter ones.

SL65 (and maybe the Maseratis) is the only one on the TA list that is heavy enough to become a really good Hot Pursuit car. Bentley and Bugatti are well-known heavy hitters of Tier 4/5.

The consideration of weight is more important should you wish to play a game of attrition or melee combat with the cops, and in Hot Pursuit in general because of the fixed route (or you can just pick the TA car and pray for a flawless run). Interceptor/Most Wanted are more tolerant to the light and agile play style.