Two very different destinations. Rhodes is the Knights' island with its UNESCO medieval old town. Halkidiki is Macedonia's green peninsula with pine-covered shores.
Rhodes wins on historical heritage. But Halkidiki hosts Mount Athos and ancient monuments on the Aristotle Trail.
Rhodes has pebble beaches and windy coasts. Halkidiki has white sand beaches and shallow waters.
Halkidiki → 1 hour from SKG airport, no domestic flight. Rhodes → international airport but isolated. See travel from Sofia.
Halkidiki is generally cheaper. See food prices.
For history → Rhodes. For tranquility, pines, easy access → Halkidiki.