But if the driver was designed for the larger box, wouldn't it be capable of higher output than a driver in smaller box?
Both the Revel and Velodyne were designed for use in their specific enclosure size.
Are you asking if a driver designed for and used in a large box will be able to play louder than a different driver designed for and used in a small box?
It would depend on the T/S parameters of the drivers. For example: the Revel and Velodyne might have the same diameter voice coil, but how long is the magnetic gap? How long is the coil? Is the coil underhung or overhung? What is the sensitivity of each driver? How do the non linear distortions of the two drivers compare? What is the actual SD of each driver? You'd be surprised of the variation among "same" size drivers!
For the sake of argument, lets play with WinISD! Let's use two drivers that require different box sizes and have similar specs. (Specs meaning both what Revel and Velodyne have released about their subwoofers. The T/S parameters will differ..just as the Revel and Velodyne no doubt differ.)
Revel says their driver can handle 2,000 watts RMS and Velodyne says their driver can handle 1,250 watts RMS. Neither company gives SD or sensitivity so the power handling is almost completely useless for comparing! If the Velodyne is 3db more sensitive than the Revel, the Revel will need 2,000 watts to play at the same SPL as the Velodyne at 1,000 watts! Likewise, if the Velodyne is 4 ohm and rated as 90db/ 1 watt and the Revel is 8 ohm and rated as 90db/ 1 watt the Revel will need 2.83 volts to play at the same db level as the Velodyne using only 2 volts.
Revel and Velodyne both give VC size. Both come in at 3".
With a bit of searching I found 2 comparable drivers, the Dayton TIT400C-4 and the Dayton RSS390HF-4. Both are 15" drivers rated as 4 ohm, both have similar power handling, and they both have the same size voice coil. As far as the Revel vs Velodyne comparison goes, this gives the large box driver a "leg up" (if the big box theory is correct) as we now know both drivers have the same impedance whereas before it was a mystery!
The RSS390HF-4 extends lower (30hz) in a sealed box than the TIT400C-4 (40hz), but that is irrelevant as both the Revel and Velodyne claim to play down to 20hz, and this demonstration is about loudness not whether ported or sealed is better for any given driver. I limited the frequency range to 100hz as I wouldn't use a sub much higher. The TIT400C-4 has a pretty narrow response in a sealed box. It rolls off 3db at ~200hz, but this is, again, irrelevant. The RSS390HF-4 extends much further than 200hz.
The RSS390HF-4 is in a 252.00 liter enclosure.
The TIT400C-4 is in a 149.5 liter enclosure.
Frequency Response from 30-100hz
Xmax @ 800 watts
TIT400C-4 xmax 20.5.
RSS390HF-4 xmax 14.0
Max SPL
As can be see from the graphs, the TIT400C-4 has a greater maximum SPL than the RSS390HF-4. At 800 watts the RSS390HF-4's xmax is reached at about 42-43hz, 12-13hz higher than its -3db point, while the TIT400C-4's xmax is reached at 30hz, 10hz lower than its -3db point. At the TIT400C-4's -3db point, 40hz, xmax is far from being reached. You could easily use a high pass filter so as to increase power handling, but you limit frequency extension further.
While the response of the TIT400C-4 could be smoother in a large vented box, for demonstration purposes I put it in a small sealed enclosure. Both drivers were put in their respective PE recommended enclosures.