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243 Winchester is far more powerful/energetic than 44 Magnum. The heaviest +P+ high velocity 44 Magnum is about 40% less energy than most loadings of 243. They both have their advantages though, 44 Mag out of a rifle has much less recoil than 243 and inside 100 yards 44 will definitely take a deer. At longer range though 44 Mag cannot contest the accuracy of 243 at all.

Shaun, yes Sir the 243 has more energy. The 243 bullet is more aerodynamic and will be superior and carry velocity/energy further as well compared to the 44 Mag. 44 Mag in a rifle details here : https://www.chuckhawks.com/handgun_rifle_cartridges.htm