I've spent the past month running both tools through my own research workflow—a systematic review of AI-assisted diagnostic tools in radiology, plus a grant proposal for a related project. Here's what I found.
The Short Version
If you need to write, brainstorm, or code, ChatGPT is the obvious choice. If you're doing structured literature reviews with specific statistical extraction, Elicit wins hands-down. But neither tool does the other's job well.