I moved your new question to your previous topic, as it is the same question of differences between Brainstorm and EEGLAB in time-frequency analysis.
Another of your related posts: How to get rid of activity before zero in time frequency plot?
If the method is different, it is normal to obtain different results (Morlet wavelets vs multitaper).
If you use exactly the same method, then you should still observe differences in the results because of the differences in implementation. If you want to check how Morlet wavelets are implemented in Brainstorm:
https://github.com/brainstorm-tools/brainstorm3/blob/master/toolbox/timefreq/bst_timefreq.m#L454
https://github.com/brainstorm-tools/brainstorm3/blob/master/toolbox/timefreq/morlet_transform.m
https://github.com/brainstorm-tools/brainstorm3/blob/master/toolbox/timefreq/morlet_wavelet.m
Ideally, no matter what measure you use, you should obtain similar results at the level of the group-level statistics. What is relevant is not so much the actual value given by one metric or another, but to know whether the difference of this measure taken between experimental conditions or subject groups is significant.