The main difference is the absence of a planetary gear set acting as a power split device in the Honda eCVT transaxle. The Toyota eCVT transaxle has no clutches of any kind.
The Honda eCVT transaxle has three modes:
An EV mode where the car is propelled only by one motor-generator (MG2). It receives energy from the battery.
ICE mode where the clutch is engaged and the ICE is coupled to the driveshaft.
Hybrid mode where the ICE rotates a generator (MG1), which charges the battery from which a motor (MG2) gets power to propel the vehicle.
In contrast the Toyota eCVT transaxle has a planetary gear set at its core that acts as a power split device with seamlessly shifting flows of energy from the battery to the wheels, from the ICE to the wheels and the battery via the generators and from the wheels to the battery via the generators. It has two motor-generators, the larger one of which is connected to the driveshaft and the smaller one that turns the sun gear of the planetary gear set determining the speed difference between the driveshaft and the ICE. The smaller one also starts the ICE when needed.
I have no personal experience driving a Honda with the eCVT transaxle but I have a Lexus hybrid. The operation of the power split device is very smooth. At very low speeds, there can be a barely noticeable jerk when the ICE comes online, though. Otherwise it's hard to notice the ICE starting or stopping because the noise insulation is that good on the GS.
As for the reliability of these two systems, I have no information. But if I had to guess, the Toyota Hybrid System is probably somewhat more reliable owing to everything being mechanically connected at all times. No oil pressure powered actuators exist and thus no hydraulic system, no solenoids to potentially fail and the overall system design is simpler.
The Toyota Hybrid Synergy Drive is analogous to the Tesla Octovalve, an eight-way valve that is part of the heat management system whose purpose is to heat and cool the drive train components and the cabin as needed, in that the system has few physical components but brilliant design allowing it to cover all operating modes efficiently and reliably.
Here's a video about the Tesla thermal management system: