What they share
Both are long, classical European names. Both carry strong meaning (Sophia means 'wisdom'; Isabella is a Spanish/Italian form of Elizabeth meaning 'pledged to God'). Both have warm nicknames (Sophie, Soph for Sophia; Bella, Izzy, Belle for Isabella).
Pick Sophia if…
Pick Sophia if you want a tighter, more international sound. Sophia travels the globe with ease (it is a top-ten name in nearly every European language). The meaning 'wisdom' gives it real philosophical weight.
Pick Isabella if…
Pick Isabella if you want warmth and flexibility. Isabella scales down beautifully to Bella, Isa, or Izzy depending on context. It has a slightly more storytelling, romantic quality than Sophia.