How well can you handle long steep grades? Both have white knuckle long steep grades. Some 14 miles of it. 120 have more than 100 of those hairpin curves.
Least difficult approach from LA is via I-5, then 99 and through South Entrance via Fresno.
Fastest is 395 but steep grades over high elevation can make your tow vehicle strain a bit (or a lot, defending on your tow vehicle-to towed unit weight ratio plus the wind drag).
Have a safe trip. Watch for the trailer push going down steep hills particularly the Grapevine (if you are going that way). I kept my speed at 55mph and shifted down to 4th or 3rd with intermittent braking.
But Yosemite to Toulumne is always worth it.