The distance between the tweeter and woofer peaks in the step response is simply a function of the crossover frequency and the filter order.the MTM have deeper bass as the LP6. and in this test there is no bass play. you hear only guitar and drums. but if you think its a bass problem i have do step response from 300 hz upto 3 khz. the results are the same. lp6 is lots slower. see setting for measure. it play only sine wave from 300 hz to 3 khz.
The higher the crossover frequency, the closer the tweeter and woofer peaks (in the step response) are together.
The higher the filter order at the crossover frequency, the greater the phase shift and thus the spacing of the peaks (in the step response).
The LP6 has a crossover frequency of 1.5kHz, the MTM one of 3.1kHz - this alone explains the differences.
In addition, the MTM offers a "linear-phase crossover at 3.1 kHz with variable edge steepness", which eliminates the phase shift at the crossover frequency and "saves" a few fractions of ms.
If the LP6 also had a crossover frequency of 3.1kHz, the difference in the tweeter and woofer peaks would be only minimally different from the MTM.
What you think you perceive as a difference in sound is most likely due to other causes, such as FR and directivity.