Hurricane and land-based severe convective weather/tornado chasing are rather different animals.
Tornadoes develop on much shorter timescales and may not always develop, even from a seemingly intense supercell in favorable conditions. With hurricane chasing, you know you're going to have a storm. With tornadoes, they and their parent supercells haven't formed yet when you make your target. You don't have days of modeling their potential tracks, they can take sudden turns (See: El Reno) but more often than not move with the parent supercells.
The objective of tornado chasing usually isn't to put yourself in the core of strongest winds, unless you're in a vehicle like the TIV or Dominator (Again, see: El Reno).
With tornadoes, you don't have to contend with surge, and you usually don't run the risk of being trapped in a disaster area for potentially several days, with blocked roads, no power, and no open gas stations for 50 miles in any direction.