Use the industry window, load a blueprint with ME/TE research selected. Switch to the Facilities tab and filter for structures with research/invention services. Show structures within skill range and sort by ME or TE research index. Hover your mouse over the ME/TE research icons and check for rig bonuses in the tooltip. Switch between different structures to see their impact on research time directly.
If you use one of the structures that does not belong to Mogul or ICY, good luck with that structure staying alive long enough to complete in particular long research jobs like ME10 research. I have had to abort several jobs and wait out asset safety for a couple of jobs now in structures that did not belong to the big blue ball or because thee fuel ran out, the service turned off and I could not contact the holder.