Si waveguides may give you higher confinement and can potentially be made more compact than LiNbO3 waveguides. On the other hand LiNbO3 has strong quadratic nonlinearity and can be used for switching applications even at low pump powers: https://www.researchgate.net/publication/230626655_Temporal_dynamics_of_all-optical_switching_in_quadratic_nonlinear_directional_couplers
Article Time-Resolved Ultrafast All-Optical Switching in Directional...
From a fabrication point of view, if you want to make narrow waveguides using electron beam lithography, it will be much harder with LiNbO3 because the material is non-conductive. Such materials "charge" under e-beams and cause placement errors. Placement errors means the electron "writing" is not happening where you want it to happen. Ofcourse there are solutions to this problem, but there are also trade-offs. If you do not intend to use electron beam lithography, then no need to worry about the above.
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