I have a lot of personal experience with two Larsen-Davis meters: The 800B and the LxT1. My 800B has a rise time of 13 microseconds, has an analog detector, and digital post processing. The LxT1 is guaranteed to have a rise time of 30 microseconds or better, and the maximum with a digital detector is 28. Both have the correct 1/4" random incidence microphone for the meter. The 800B and B&K 2209 have pretty much the same peak detector (better than 20 microsecond rise time).
At Gemtech last year, we had a B&K demo with their pulse system, although the mic they used (1/4") had a rise time of 6-7 microseconds. Interesting results. The 800B, 2209, and LxT1 are self-contained handheld meters. The Pulse is bulkier.
Unweighted (which is probably the most correct method) showed that the 800B read 4 dB low compared to the pulse and the LxT1 read about 9 dB low. Compared to the 800B, the LxT1 read 5 dB low. This is to be expected based on rise times and the sharp slope of the firearm peak.
However, with C weighting, The 800B read 1 dB low compared to the pulse and the LxT1 read 1 dB low compared to the 800B. The explanation is fairly simple: The weighting networks degrade the meters to match the frequency response of the human ear, and they essentially cut off at a little over 25-30 kHz. Weighting networks, in essence, degrade the meters to around 30 microsecond rise time.
MIL-STD has traditionally specified a rise time of 20 or better, but permits either A or C weighting, which I believe to be ill advised when considering hearing damage risk. When one installs a suppressor on a barrel, the suppressed barrel has to still dissipate the same amount of energy as non-suppressed, but the suppressor reduces the pressure (through primarily volume expansion) and spreads out the time-exit curve through internal turbulence and momentary baffle trapping. The result is a broader, more spread out and lower intensity peak with a more gradual slope.
The B&K Pulse unit is very expensive with the microphones and accessories (around $25K). This includes expensive software and a laptop is necessary. Fully decked out, it is portable, but not nearly as compact as a hand-held meter. Both the LD 800B and the B&K 2209 are long out of production, and as they age, repair parts are becoming really scarce. LD keeps rapidly dwindling trade-ins as a source of replacement boards.
The LxT1 is current production, is handheld, and runs on a set of AA batteries.It has a lot of features that qualify it as a precision meter for environmental measurements, and it has the best of the currently available peak detectors in handheld instruments. While not absolutely perfect for our purposes, it is the best available in portability and price point (around $3,000).
As long as A- or C-weighting are specified or permitted, the LxT1 is the best bet as a substitute for the 800B or 2209 if you keep in mind that it will read one to two dB low. Nothing else in its price range or portability will do the job. There are a lot of industrial sound meters available that are tempting, but not all have a peak detector (not the same thing as an impulse detector), and those that do have a rise time greater than 50 microseconds (which gets you well into the error region).
Please remember as you find an 800B or 2209 on eBay, these meters are over 25-35 years old and may no longer meet their original specs or be repairable. And few come with the correct microphone; most will have a 1/2" mic that definitely will not be adequate for firearm sounds. And, of course, you will need a calibrator which will run a couple of hundred dollars.