Per Google Maps, travel time is slightly less (just under 3 hours) via shinkansen to Itami, which requires a bus transfer from Shin-Osaka Station. Kansai is just over 3 hours (about 20 minutes longer). Because the distance to Kansai is significantly greater (with greater average travel speed), the ticket cost is significantly higher. So Itami seems to be the better choice.
There are also other flights that require connections so price would be more.
Hiroshima airport thought is a fair distance from Hiroshima so you have to allow sufficient bus time, but it certainly will be cheaper than taking train to Osaka area.
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