Some simple comparisons:-
-200 vs -300.
-200 published schedule Brisbane to Honiara v.v: 3 hours 40 minutes.
-300 published schedule Brisbane to Honiara v.v: 3 hours.
assuming ground times the same for both, an extra 40 minutes flying time in a -200.
-200 fuel burn Brisbane to Honiara v.v: 8.5 - 9.5 tonnes (conservative??)
-300 fuel burn Brisbane to Honiara v.v: 7.5 - 8.5 tonnes
at some 70/litre ex Brisbane = around $900 extra in fuel costs for a -200.
-200 payload Brisbane to Honiara: 9 tonnes.
-300 payload Brisbane to Honiara: 12 tonnes.
equates to 30 more passengers and their bags in a -300.
Now, thirty extra passengers and bags or 3 tonnes freight (or combination thereof) for at least $900 less in fuel costs per trip would seem to indicate the -300 is a better choice.
What on earth possessed Solomon Airlines to pick such an aircraft for their services? Sure, an improvement over the E-170, but not as good (or as economically sound) as the alternative available (and I'm assuming, offered).