The whole way Wilkinsons work has been extensively discussed in this forum.
Searching "Wilkinson" will yield all of them.
Essentially, the use of the 100 ohm resistor spectacularly improves the performance, but the whole idea relies on it being used such a way that the phase and amplititude of the signals at each end of the resistor are the same, so that the resistor does not run any current, and does not dissipate anything. Then, the killer feature is the very high isolation between the ports across the resistor. The ports cannot see each other, so each may be connected to an antenna, knowing that what comes in one port cannot be leaked back out the other and re-transmitted away. BUT .. the input signals must be phase coherent, from identical path phased pair.
There is a variant (see Gysel) which uses separate resistors as terminations in a structure similar to the "Rat Race" splitter / combiner. This can be more convenient to make because there is no need to bend or change direction in the tracking to get the lines close enough together to meet a resistor, and it takes away the issue of the physical size of the resistor structure and it's lands affecting things when the frequency gets high > 2GHz
The use of these splitters / combiners is great for splitting a signal, then amplifiers in each route, then re-combine. High power can be had from two low power kits, and the failure of one will not stop service. It just lowers the level by 3dB until the dead one is fixed.
For patch antennas, you can split a single patch signal just fine, but if you want to feed / receive with two patch antennas, you need that the signal from each is identical - a phased array of patch antennas. Signals coming from the side, arriving at one before the other, will not combine as you might expect. This is probably true for most types of combiner that depend on resonant quarter-wave features.