HDPE vs PET bottle for shampoo. Do they have any effect on stability and preservation?

I am currently using HDPE bottles for shampoo but as PET Bottles are less expensive they attract me.

Shampoo has water, SLS, SLES, CAPB, APG, cationic guar, PQ10, Amodimethicone emulsion, phenoxyethanol, caprylyl Glycol, Piroctone Olamine, fragrance oil, EDTA, xanthan gum.

Does HDPE has any advantage over PET in stability or preservative of shampoo with these ingredients? 
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