Hi Nathalie,
Preservation value is more reliable with white refined sugar than it is with honey mainly because it has been refined. Honey is a great preservative due to some of the compounds that are naturally found within it, however it’s also less refined/controlled and if you are using raw honey (what I would recommend) there can be various components in that honey (including yeasts or bacteria). There is also water in honey which is the best conduit for life growth, where there is not in white sugar.
So ultimately for consistency and reliability white sugar is the best preservative. I still choose to use honey for most of my syrups though and it works very well, especially if kept in the fridge and the person using the syrup uses caution with how they pour it out (e.g. they are not ‘double dipping’).
I hope that clarifies things a little bit.
Benna