Palestine is better pronounced. It becomes Falastin and very much compatible with the Arabic language, unlike Bebsi.
On the etymology of the word "Palestine" from Wikipedia:
The term "Palestine" (in Latin, Palæstina) is thought to have been a term coined by the Ancient Greeks for the area of land occupied by the Philistines, although there are other explanations.
The English term Philistine comes from Old FrenchPhilistin; from Classical LatinPhilistinus; from Late GreekPhilistinoi; ultimately from HebrewPəlištî (פלשתי; plural Pəlištîm, פלשתים), meaning 'person of Pəlešeth [פלשת]'; and there are cognates in Akkadian Palastu and Egyptian Palusata; the term Palestine has the same derivation.
Outside of pre-MaccabeanIsraelite religious literature, evidence for the name and the origins of the Philistines is less abundant and less consistent. In the remainder of the Hebrew Bible, ha-Plištim is attested at Qumran for 2 Samuel 5:17. In the Septuagint, however, 269 references instead use the term allophylos ('of another tribe').