The SL1300 is the better turntable but the crux of sound quality in vinyl playback is the cartridge compliance quality, frequency response at a given capacitance and VTA.
the Audio-Technica 440MLb is good for compliance with the SL1300 tonearm but its frequency response is tilted bright for most capacitance loadings
So, you need a new cart with the SL1300 regardless - https://www.audiosciencereview.com/forum/index.php?threads/introducing-the-phono-cartridge-measurement-library.46108/post-1819037
This cartridge is what to get in addition to the SL1300 @naish - Shure V15 Type V-MR MM Phono Cartridge - Complete Kit