OpenAI is far ahead of Anthropic in many ways, but I've got to say that I MUCH prefer talking to Claude. It has a pretty distinct personality that I enjoy, much more than any of OpenAI's models (even with extensive prompt engineering).
There are some things it does that annoys me (it almost ALWAYS ends its response with a question, and it falls back to the "I aim to be respectful and genuine blah blah" responses a bit too much), but overall Anthropic has done good work with making Claude fun to talk to.