This sounds not right. I'm worried that you have not kept your range of prices consistent across the runs.
For example, let's imagine the range from lowest possible to highest possible prices is $1,000 to $5,000.
For the Linear Price model, you should go to the Attribute Coding tab and then click the Price attribute to reveal the panel to the right (Price Values) that has 30 cells in it. If $1,000 to $5,000 was the total theoretical range of prices, then you should have a $1,000 in cell 1 and a $5,000 in cell 2.
Now, when you do your log-linear price model, you need to represent more prices along the continuum in the Level Values table to make sure that the "bend" from the log-linear curve makes its way into the market simulator. So that can happen, you must specify additional price points in between $1,000 and $5,000. So, I'd recommend you use at least 5 price points in the Price Values table: $1,000; $2,000; $3,000; $4,000; $5,000. Change the coding method for the attribute to Log-Linear. Now, run HB again.
For piecewise, you again need to specify more than 2 price levels in the "Price Values" table. Again, you could use $1,000; $2,000; $3,000; $4,000; $5,000. Change the coding method for the attribute to Piecewise. Run HB again.
If you continue to see significant difference in your price importances under the different coding schemes, you really should send your project into our tech support group and let them step through this with you.