The Rega will probably be a bit more lively/fast and the Music Hall a bit more smooth/warm. But honestly my approach with turntables is they all sound so good that you're better off focusing on functionality like do you want a dust cover, VTA, how does the tone arm feel, condition/build quality, things like that. Because ultimately you will be able to make it sound pretty much however you want by changing the cartridge.
Then as far as sound goes its usually better with budget gear to err on the side of smooth/warm.
Then as far as sound goes its usually better with budget gear to err on the side of smooth/warm.