A common opinion expressed is that sealed subs are "faster" than vented, and it's often argued that this is related to their transient response. I'm going to argue a case for vented subs when used in a particular way and it won't suit everyone. There are some important facts that are typically overlooked in the often overly simplified arguments that are frequently made on internet audio forums.
Sealed vs vented subs outdoors
When measured outdoors or in an anechoic chamber, sealed subs tend to have better time domain performance. A vented sub will have some ringing, as seen here:
You can see the port causes a much slower decay when compared to the same driver in a sealed box as shown below:
To put these into perspective, a 20db drop in level means only 1% of the output remains. So in this context we can compare the time taken for a 20 db drop, denoted T20
What happens in a real room?
When placed in a room, the room itself will start to interact as well. Room modes will cause their own ringing, and this will generally be much worse than either sealed or vented subs.
In a typical room it will take around 250ms to achieve T20. Both of the charts above only show down to 200 ms and in both cases, it's off the chart. So even the vented version which has some ringing is actually not the bottleneck - the room is. It should also be noted that this ringing occurs down low where sounds reproduced are most likely to be artificial LFE content and not critical. In the range that deals with instruments, there is no real difference.
So why do they sound different?
Usually there are numerous differences going on simultaneuously and that makes it difficult to pin anything down. A common mistake is to pick just one thing and pin it down as the cause - often something like transient response or group delay which are real and measurable but often more than likely not the audible cause of difference.
The first suspect is frequency response and room transfer function. A sealed sub will have more roll off and this will tend to sound a bit tighter, and when combined with room modes can often yield a better raw response. But if both are equalised flat in room the main differences are likely to quickly disappear.
There are other issues involved here, but I think we can rule out transient response in most rooms.
A dynamic solution
My reason for making this point is that I often see sealed subs chosen for their perceived improvement where a vented design could be made to work better. To do the same job with a sealed driver requires more power and excursion due to the loss of efficiency. More power means more power compression which can be a backward step for dynamics. More excursion also has it's downsides and will also tend to further reduce efficiency. So there is a performance and financial cost involved.
Efficiency and dynamics go hand in hand. A solution I suggest for music applications is a vented active woofer. Aim for a driver with a fs around 40 Hz, decent excursion and high efficiency. Tune around 40 Hz then use EQ to get the in-room response right. Many pro woofers with about 9mm xmax are ideal choices, with about 95 db efficiency. With about 200w you will see about 118 db before compression. Try to get the same result with a sealed woofer and you will lose 12db of efficiency. The typical solution is a HT sub driver, but you will need a lot more power, a very expensive high excursion driver at many times the cost. An equivalent result is possible only with a major cost blowout. A better choice would be a higher quality driver.
Don't dismiss vented alignments
Avoid this mistake. A sealed woofer can be more of a plug and play solution, but also consider the cost in terms of efficiency.