They are about the same distance from the airport.
If you are travelling to the airport, you can take a taxi or take the lightrail to Metro/Airport and then a free shuttle to the airport terminals. At the San Jose Diridon station, the lightrail is right there - Amtrak and lightrail use the same station. At Santa Clara, you will have to walk a half block or so to Tasman station to get the lightrail. You don't want to take Caltrain to the airport though - it runs less-frequently than the lightrail and you would still have to take the shuttle to the airport terminals.
If you want to take Caltrain up the peninsula, then San Jose Diridon station is best because Amtrak and Caltrain both use the same station.
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