Operation with better feedback from the thermostat should always give performance that is as good or better than operation without as much feedback. The obvious trade-off is that installing more stages of control may mean running extra wire which may not be easy to do.
If you have a two stage Ecobee3 and you can connect it to the furnace and set the furnace for two stage control, then that should be an improvement over the furnace controlling its own staging, which is usually just a timer that runs the furnace at stage 1 for awhile and then switches to stage 2 if that does not satisfy demand.
I do not know exactly which Keeprite model you have, but the self-control scheme for a single stage thermostat signal is probably similar no matter the model. Here is an excerpt from the Keeprite G9MXT installation guide:
For single_stage thermostats, connect thermostat W to W/W1 at furnace control terminal block. (See Figure 7) For single_stage thermostats, the control will operate for 12 minutes on low heat, then switch to high heat if heat call remains. Setup switch (TT) must be in the factory_shipped OFF position. See Figure 7 and Figure 15 for setup switch information.
If a two_stage heating thermostat is to be used, move setup switch (TT) to ON position before starting furnace. This overrides built_in control process for selecting high and low fire and allows the two_stage thermostat to select gas heating modes. The W2 from thermostat must be connected to W2 on control terminal block.
The ultimate in precise control is a digital communicating thermostat if your furnace has that capability.