To Print Booklet to a PDF you have to use a Postscript or Distiller workflow, which flattens transparency and has few reliable color management options. A regular PDF Exports has none of those limitations. A Postscript workflow would have problems converting colors. Does the gradient use RGB, Spot, or Lab colors; or include transparency?
Rob is correct that the Print Booklet output of PDF via the Adobe PDF PostScript printer driver instance is different from the PDF created via direct export.
Personally, I advise InDesign users to never print directly from InDesign, but rather to export PDF/X-4 and print from Acrobat.
For purposes of booklet creation, a much more reliable option is to directly export pages (not spreads) from InDesign using the PDF/X-4 preset. If you are going to a commercial printer, in general, it is the responsibility of the printer to impose your pages to yield a booklet; that's part of what you are paying for. I'd be very wary of any commercial printer who claims that they can't do this or that they want to charge extra.
Alternatively, if you are doing the printing yourself, you have two options:
The first is to use built-in booklet printing capabilities in your printer itself. Many high end PostScript and direct PDF print devices provide booklet printing as an option. If your printer supports this, there is no cost to you.
The second is to obtain a plug-in to Acrobat to impose the pages into a booklet. There are a number of third party plug-ins that do this reliably including Quite Imposing and PDF Snake.
Setting the booklet output to a postscript file and then converting it in Distiller works.