Miniature omnis as a group have the highest SPL limits of all mic types. It’s large diaphragm mics that more often have high SPL problems. Generally the smaller the diaphragm, the higher the SPL limit can be.
Most miniature omni manufacturers make several different sensitivity versions of their mics, including low sensitivity versions with SPL limits higher than anything most tapers would ever need for recording music into the gear we use. As others have mentioned, the high SPL trade off is generally less sensitivity and more self-noise as the high SPL limit is increased, sometimes less overall dynamic range capability (meaning that the noise floor may increase a more than the upper SPL limit does, but that's mostly a technicality).
Of the two evils, clipping or distortion due to high SPL is worse than noise on the quieter stuff. That's partly for the reasons the others have described (the self-noise of the mics is often less than the recording environment anyway) and partly because a bit of hiss on the low parts ain’t so bad compared to distortion or outright clipping.. the music is still there, and we used to use hissy tape anyway. Pops and clicks are now retro-cool on LPs, is tape hiss next?!
Best way to maximize the SPL handling of any given mic is to power it properly. Sometimes modifications can be made to an existing mic, like wiring with source resistors to lower the sensitivity and increase SPL handling. Keep in mind that it’s not always the mic itself that is the source of distortion. Sometimes a sensitive mic is within it’s own SPL limits but overdrives down-stream input circuitry with too much output. I’ve had that happen with 4060s.
Specific mics-
As far as I'm aware, Countryman offers the B3 in two different sensitivities- high and low sensitivity. DPA offers three different sensitivity levels- 4060 highest, 4061 lower, 4062 lowest and I've never heard of any tapers using those, they certainly aren’t needed for music recording. Not sure about Sennheiser, or the other big manufacturers. As for the small manufacturers, Guy at Sonic Studios makes his DSM mics in a large number of sensitivities. Presumably those mics have a smaller overall dynamic range so he offers many different sensitivity options. Chris churches’ mics are pretty low sensitivity and are pretty much all designed for amplified music at typical SPLs.
Conveniently the color code is similar between the two common sensitivity versions of the Countryman and DPA models:
The high sensitivity B3 and the 4060 have white serial number tags.
The low sensitivity B3 and the 4061 have red serial number tags.
I’ve used the high sensitivity B3, the 4060 and the 4061.
In my use (mics powered properly) and to my ears, the 4060 has the lowest perceptual noise floor.
It also has a higher SPL limit than my (high sens) B3s, but keep in mind that my B3s are wired directly to the connector as suggested by Countryman. Many here at TS suggest wiring the B3s with source resistors to increase the SPL limit and limit distortion, at the expense of some sensitivity and added noise. I have not compared the apparent noise floor of the high sensitivity B3 and the 4061.
Hope that helps.