The new provision provides:
319AA. Dangerous or negligent driving while pursued by police
(1) A person must not drive a motor vehicle dangerously or negligently if he or she knows, or ought reasonably to know, that—
(a) he or she has been given a direction to stop the vehicle by a member of the police force; and
(b) a member of the police force is pursuing the vehicle.
Penalty: 3 years imprisonment.
(2) For the purposes of subsection (1)—
(a) a person drives a motor vehicle dangerously if he or she drives the vehicle at a speed or in a manner that is dangerous to the public having regard to all the circumstances of the case; and
(b) a person drives a motor vehicle negligently if he or she fails unjustifiably and to a gross degree to observe the standard of care which a reasonable person would have observed in all the circumstances of the case; and
(c) a member of the police force may be pursuing a motor vehicle even if not travelling at the same speed as the vehicle; and
(d) it is irrelevant that the police pursuit is suspended or terminated before the motor vehicle being pursued stops.
(3) In this section—
direction to stop has the same meaning as it has in section 64A(5) of the Road Safety Act 1986;
motor vehicle does not include a vessel.
In addition to the more severe sentencing options, there are also longer licence cancellation and disqualification provisions added to Sentencing Act 1991 s 89(1AA), starting at 12 months, in contrast to 6 months for the vanilla pursuit offence.
Following the High Court's decision in King v The Queen (2012) 245 CLR 588 at  (see our post on that case here), the distinction between dangerous and negligent driving is stark.
At 605 , the Court said,
The ordinary meaning of “dangerous” is “[f]raught with or causing danger; involving risk; perilous; azardous; unsafe”. It describes, when applied to driving, a manner or speed of driving which gives rise to a risk to others, including motorists, cyclists, pedestrians and the driver’s own passengers..
The Court went on at 609  to endorse the test for dangerousness in Jiminez and McBride. In Jiminez at 579 , the High Court said:
For the driving to be dangerous for the purposes of s 52A [the NSW provision under consideration then] there must be some feature which is identified not as want of care but which subjects the public to some risk over and above that ordinarily associated with the driving of a motor vehicle, including driving by persons who may, on occasions, drive with less that due care and attention.
In McBride at 50 :
This concept is in sharp contrast to the concept of negligence. The concept with which the section deals requires some serious breach of the proper conduct of a vehicle upon the highway, so serious as to be in reality and not speculatively, potentially dangerous to others. This does not involve a mere breach of duty however grave, to a particular person, having significance only if damage is caused thereby.
Negligent driving is similar to civil negligence — in the sense that it requires establishing the elements of negligence: duty of care, breach, and harm resulting from that breach — but further requires that the negligence is of a degree deserving of punishment by the criminal law: King v The Queen (2012) 245 CLR 588 at  – ,  – .
I've always found the House of Lords' decision in Andrews v DPP  AC 576 helpful when understanding what criminal negligence is. (That case was cited with approval by the High Court in King v The Queen at .)
In Andrews, Lord Atkin said at 538:
Probably of all the epithets that can be applied "reckless" most nearly covers the case. It is difficult to visualize a case of death caused by reckless driving in the connotation of that term in ordinary speech which would not justify a conviction for manslaughter: but it is probably not all-embracing, for "reckless" suggests an indifference to risk whereas the accused may have appreciated the risk and intended to avoid it and yet shown such a high degree of negligence in the means adopted to avoid the risk as would justify a conviction. If the principle of Bateman's case is observed it will appear that the law of manslaughter has not changed by the introduction of motor vehicles on the road. Death caused by their negligent driving, though unhappily much more frequent, is to be treated in law as death caused by any other form of negligence: and juries should be directed accordingly.
These tests are contained in s 319AA(2), albeit differently expressed, and it's pretty clear from King v The Queen that the High Court will insist on Courts following the words of the statute.
Very few pursuits are likely to involve driving that is not allegedly dangerous or negligent (or both). The exception might be a low-speed pursuit in something like a tractor or golf-buggy. Which offence will prevail remains to be seen, especially given the High Court noted in King v The Queen at 609  that, "It may be that in many if not most cases dangerous driving is a manifestation of negligence in the sense of carelessness."
The second reading speech and explanatory memorandum suggest that the main motive of the new offence was to create an indictable offence — with all the arrest and entry powers that accompany that — and increase the penalties available to the Courts to act as a deterrent. (Despite the likelihood that a person fleeing the police is more focussed on escaping, rather than consequences, even thought they might be motivated by escaping the consequences of their driving.)