In very high SPL situations, the 4060 will eventually clip before a 4061. SPLs of that level of intensity are very, very, loud - like causing permanent ear damage loud. However according to the DPA specifications, the distortion produced by the microphone prior to reaching SPLs that level isn't significantly different between the two.
These mics do not roll off the bass, they are flat to a very low frequency. Note that a microphone's physical size has no relation to its low frequency sensitivity, and these will pull as much bass as any full sized omni. The few times I've experienced distortion using 4060, its been the low bass content range where the SPLs have been high enough to cause audible distortion.
Because the 4060 has a considerably higher sensitivity than the 4061, it will produce a significantly hotter output for the same SPL. So sometimes it's not the microphone itself but the following component (preamp or recorder) overloading and causing the audible distortion. I've had more instances of distortion caused by insufficient preamp battery voltage than by the mics themselves distorting. But in the end a distorted recording is a distorted recording, and it matters less where that distortion occurs than that it is occurring in the first place, unless you can address and correct for it next time (by changing the preamp or it's battery or whatever).
Given that, choosing the 4061 is a safer bet if you occasionally record very very loud stuff, as long as you aren't concerned with also occasionally recording very, very quiet stuff as well. If you want to record really quiet material where you can hear the person next to you breathing too loudly, the 4060's lower self-noise and higher sensitivity make it more suitable. Either will do just fine for most recording situations, which generally lie between those two extremes.
Here's the relevant differences in specification between the two-
DPA 4060
Sensitivity, nominal, ±3 dB at 1 kHz: 20 mV/Pa; -34 dB re. 1 V/Pa
Equivalent noise level, A-weighted: Typ. 23 dB(A) re. 20 µPa (max. 26 dB(A))
Equivalent noise level, ITU-R BS.468-4: Typ. 35 dB (max. 38 dB)
S/N ratio (A-weighted), re. 1 kHz at 1 Pa (94 dB SPL): 71 dB(A)
Total harmonic distortion (THD): < 1% THD up to 123 dB SPL peak; < 1% THD up to 120 dB SPL RMS sine
Dynamic range: Typ. 100 dB
Max. SPL, peak before clipping: 134 dB
DPA 4061
Sensitivity, nominal, ±3 dB at 1 kHz: 6 mV/Pa; -44 dB re. 1 V/Pa [lower]
Equivalent noise level, A-weighted: Typ. 26 dB(A) re. 20 µPa (max. 28 dB(A)) [higher]
Equivalent noise level, ITU-R BS.468-4: Typ. 38 dB (max. 40 dB) [higher]
S/N ratio (A-weighted), re. 1 kHz at 1 Pa (94 dB SPL): 68 dB(A) [lower]
Total harmonic distortion (THD): < 1% THD up to 123 dB SPL peak; < 1% THD up to 120 dB SPL RMS sine [same]
Dynamic range: Typ. 97 dB [lower]
Max. SPL, peak before clipping: 144 dB [higher]