We learn a great deal about the performance of the Falcon in this film, and of ISDs. The Falcon appears to have somewhere around 30g of high-maneuverability acceleration, which can be altered swiftly on demand just as well as a starfighter. Linear acceleration seems similar.
ISDs have fully equal linear acceleration to the Falcon; however, they are incapable of coming to full acceleration quickly, or turning quickly.
TIE fighters and bombers are at least somewhat faster than the Falcon, although they do not appear to have superior maneuverability.
The Falcon appears capable of fairly high maneuverability, being able to turn around at full throttle in a roughly half-circle figure in roughly 3 seconds. If the circle is a bit over a half kilometer wide, this would place the Falcon's unaided acceleration at ~30g; if a full kilometer wide, ~56g. This occurs shortly before an approach in which the Falcon spent 2-3 seconds swinging to a halt after flying the length of a Star Destroyer in roughly nine seconds.
The ISD cut forward speed as the Falcon approached. Taking 1600m for the length of what bridge officers interpret as an attack run on the bridge, this represents an average speed of roughly 180 m/s. If the relative acceleration was constant during the attack run, the final speed of approach could have been as high as 360 m/s relative to the ISD. In this case, the relative acceleration between the two vessels is 40m/s2 during the attack run, and up to 120-180m/s2 (12.2-18.4g) while braking - in either case, not particularly high compared to the acceleration seen in the Falcon's turnabout.
Either Han wasn't going full out, or the ISD has a high reverse acceleration that was used in this run. In either case, the sum of the two accelerations is also a reasonable estimate (160-220m/s2), assuming that the ISD is accelerating rearward at full Falcon-reverse.
The ISD chasing the Falcon had no trouble keeping up with the freighter. Thus, it is as fast. However, if ISDs were capable of applying 30g on a couple seconds' notice, it would be possible for an ISD to dodge an ion cannon bolt with the flight times seen onscreen. We may therefore suggest that an ISD may not change its acceleration too swiftly. Alternately, an ISD might not have the command response time necessary to detect an ion or turbolaser bolt as a threat and then dodge it.
A near-collision at the Imperial fleet's exit from hyperspace demonstrates their turning abilities - poor at best.
The TIEs sent after the Falcon had no trouble catching up with it, or accelerating past the ISDs that launched them. Thus, they have greater linear acceleration. However, their maneuverability does not seem greatly improved from the Falcon.
9.2g in reverse
1600m? Or less?