Quick comparison
Both appeared in 1953. Both have a V12 engine. The more powerful one is the Ferrari 375 MM: 340 PS versus 280 PS. The higher top speed belongs to the Ferrari 375 MM: 289 km/h versus 282 km/h. The lighter one is the Ferrari 340 MM: 850 kg versus 900 kg.
All values come from the data sheets of the two models (sources listed there). The better value is highlighted in green wherever both data sheets give a comparable figure. Photos – Ferrari 340 MM: Klaus Nahr, CC BY-SA 2.0; Ferrari 375 MM: Prova MO, CC BY-SA 4.0. Licenses and originals: Sources & image credits.