The most noticeable performance differences come from steering and suspension changes. The ELR has a different suspenion system from the Volt -- not just differently tuned but different -- for better cornering feel and smoother driving on rough roads. The ELR's electrically assisted power steering system also provides better feel and more responsiveness, especially in "Sport" mode.
Another cool touch is the addition of "Regen on Demand" paddles on the steering wheel. They slow the car sharply by connecting the wheels to the unpowered electric motors. This spins the motors backwards which, besides slowing the car down, also generates electricity for the battery. Sure, you could do the same thing by pressing lightly on the brake pedal but it's fun to be able to "downshift" into a curve using the paddles while leaving your foot over the gas pedal.
The ELR is about a second faster than the Volt in getting from zero to 60 miles per hour when both the gas and electric motors are working together. (Acceleration is about the same as the Volt's under battery-only power.)