I was very desperate and finally i found solution. It looks like it is the pathing problem.
On my newly "mac" created gallery .xml files paths to images look like this:

<image imageURL="images/20101009_0794.jpg"
    thumbURL="thumbs/20101009_0794.jpg"
    linkURL="images/20101009_0794.jpg"
    linkTarget="_blank"
    sourcePath="/Users/Maciek/Projekty www/kolasinski.art.pl/Galerie/Podwodne_mczerwone/images/20101009_0794.jpg">
    <title><![CDATA[]]></title>
    <caption><![CDATA[Shaab el Erg (głębokość 9m)]]></caption>
  </image>

On windows created galleries it looks differently:

<image imageURL="images/20101009_0794.jpg"
    thumbURL="thumbs/20101009_0794.jpg"
    linkURL="images/20101009_0794.jpg"
    linkTarget="_blank"
    sourcePath="D:\Projekty www\kolasinski.art.pl\Galerie\Podwodne_mczerwone\images\20101009_0794.jpg">
    <title><![CDATA[]]></title>
    <caption><![CDATA[Shaab el Erg (głębokość 9m)]]></caption>
  </image>

It looks like for juicebox-builder in windows these paths doesnt matter "\" or "/". On mac is different it must be "/" instead of "\"

So the solution is to use "find/replace" to repair paths in all my .xml config files.

Permissions on gallery files are ok: Read&Write. Gallery folder is in unrestricted place, the same directory where is new created gallery built with juicebox-builder which is opening without any problem. Copying to different location gives no result.

All the issue seems to be very mysterious.

It seems the only solution will be to put a lot of effort and rebuild galleries to completely new ones.

I'm sorry to say but following strictly Your instructions did not solve the problem.

Please note also one thing that the problem appear just after first installation of juicebox on my mac. There was no any previous juicebox installation. The OS was quite fresh. All jucebox gallery files were migrated from windows computer.

Great. This workaround works good for both browsers.

Anyway,  awaiting bug fix in next version of juicebox.

Thank You for prompt reply.