In what way, other than both being old, white, rich and from New York.
Trump wanted to tack hard away from the center and to tear down the Republican establishment and rebuild it with a more populist vision. Bloomberg is running to stop the Democrats from tacking away from the center and to 'protect' the party from those threatening to tear it down and rebuild it with a more populist image.
Trump ran as an outsider populist, Bloomberg as an insider technocrat.