What is the difference between friggatriskaidekaphobia and paraskevidekatriaphobia?

The difference is primarily one of Word origin. Friggatriskaidekaphobia starts with a Greek-originated term "triskaidekaphobia" or the fear of the number 13 (triskaideka = 13, phobia = fear). It then tacks on the name Frigga, the Norse god for whom Friday (Frigga's Day) is named.

Paraskevidekatriaphobia takes it name from the Greek Words for Friday, Paraskevi, and dekatria, also meaning 13, and adding in phobia for fear.

I don't know of any differences in meaning. It is comparable to the works "guarantee" and "warranty". The both have the same meaning, but their spellings derived from different regions.

Paraskevidekatriaphobia could be considered "purer" since all terms originate from Greek, but purity has little to do with the formation of language.