m4rs-mt
I fully agree that both libraries use different approaches to realize .Net code execution on the GPU. Correct me if I'm wrong: ComputeSharp is a source->source translator for C# to HLSL (as you said) and ILGPU is an IL code->assembly just-in-time compiler for .Net programs (similar to the .Net runtime itself; except for the current implementation of the OpenCL backend...). ILGPU is designed to implement GPGPU programs highly efficiently on GPUs while having the ability to emulate all functions on the CPU for debugging (use case: HPC-inspired GPGPU computing workloads). It also includes a variety of different compiler optimizations specific to different GPU architectures. The primary focus has been to achieve high performance on NVIDIA GPUs that is comparable to "native" Cuda programs.
However, I also think there is definitely enough room for both libraries in the ecosystem (as they also target different groups of developers/users... :) ).