I'm not certain why the ACR and Lightroom versions of "super resolution" would differ.
They do not. When on version parity, the two are indentical.
Even without Super Resoution, the ACR engine should provide a better resampling up than Photoshop for a number of reasons, both resampling is a hybrid Bicubic algorithm that interpolates between Bicubic and Bicubic Smoother for upsampling and Bicubic and Bicubic Sharper for downsampling. Lightroom and ACR uses a adaptive bicubic algorithm: the algorithm parameters are chosen
automatically based on the relationship between the original image size and the final image size, from raw linear data. These parameters were determined empirically by doing lots of experiments with photos being resampled to common output sizes, such as web-sized images (800 to 1000pixels on the longer dimension), small prints, and big prints.
I can see slight improvement over the same resizing using various Photoshop algorithms. But what I see as visible improvements, others may not agree.
Having parametric edits that just get better as time goes on, and without dealing with large TIFFs (with burned in edits) is yet again why I prefer to do all of this at the raw stage. YMMV.
I agree about the halo's in that 3rd party upsizing product; not attractive to me.