score:4
The Osaka City Transport Station Guide to the rescue! Japanese only, but the station diagrams and their elevator icons are pretty self-explanatory. In both cases the red lines represent the Midosuji Line. Click on the 駅構内図を膨大 button in the top right corner to view expanded PDFs.
Shin-Osaka: has elevators both to platform and street level
Tennoji: also has elevators both to platform and street level (see PDF for a more legible version)
That said, if you can time it right the Haruka or Kuroshio will be faster and more comfortable (it's a single stop), but it also costs a lot more (¥870 in an unreserved seat, vs ¥220 for the subway) and runs less frequently.