Cars that are optimized for 87 octane (Vortec V8 in a Silverado) can benefit from more aggressive timing advance.

Cars that tend to run on the lean side of optimal at WOT on the factory tune (WRX and VQ35) benefit from richer AFR targets in regards to safety, any gains experienced here are from less detonation/the ecu not having to pull timing.

Most newer cars have dynamic timing advance. The engine is tuned for optimal performance on premium fuel but can run on 87. The base timing will adapt to the fuel quality until knock is detected and will store an adaptation to only allow a certain degree of additional timing advance from the base. The better the fuel used, the closer to optimal it will be allowed to run.

Handheld tuners on modern engines are typically going to alter the electronic throttle curves which can make a very big difference in how powerful the engine feels. 

There are a lot of other parameters that can be adjusted such as the VVT setpoint and removal of throttle tip-in timing retard that help with emissions etc. but that all depends on the car and the tuner. 

In general, for anything modern, I would only expect a handheld tuner to: richen target AFR a tad, raise rev limiter, remove top speed limiter, make the throttle mapping more aggressive, and if the car is turbocharged, raise the boost pressure.

Obviously the ideal scenario is a custom tailored dyno tune which will better suit the environment the car is in, the condition of the engine, and any changes that have been made to it, But handheld tuners like SuperChips are cheap and easy.

I would be willing to try out a SuperChips tuner but only if it was cheap and I monitored the AFR afterwards to make sure it is an actual improvement.

Economy tunes that help with gas mileage reduce throttle sensitivity. On high performance engines that normally demand premium fuel, they will have less aggressive base timing maps that allow you to run 87 octane.