I don't like focusing ones attention on importance scores, which are not as useful or meaningful as part-worth utilities or especially market simulations.
Importances are kind of a strange calculation based on the maximum difference observed between best and worst levels for an attribute, at the individual level. But, if there is an attribute with little impact for a respondent, then just random noise for the utilities of levels for that attribute will drive a positive importance score. "Reversals" (levels out of order from expected rational preferences) still are counted as a positive weight toward the importance score.
HB tends to reduce reversals at the individual-level, and should give a cleaner view of attribute impact, in my opinion.
But, you could also estimate your utilities by imposing utility constraints (monotonicity constraints) for either OLS or HB. And, that should also sharpen the importance calculation.
Again, I'm not a fan of importances.
And, the differences you are noting seem relatively small, to my eyeball.
Attributes 1 and 3 seem about tied, and attributes 2, 4, and 5 seem about tied. So, there could be some trading around of rank orders due to minor changes in the absolute importance scores.