Honestly who knows, but outside of Q-star rumors there's no indication that either company is doing anything much different from the other one, so I'd not expect any long-lasting difference in capability to open up. Maybe it will, though!
FWIW, Sam Altman has fairly recently said that the jump from GPT-4 to GPT-5 will be similar to that from GPT-3 to GPT-4, and also (recent Lex Fridman interview) that their goal is explicitly NOT to have releases that are shocking - but rather they want to have ones of incremental capability to give society time to adapt. Could be misdirection - who knows.
Amodei for his part has said that what Anthropic will release in 2024 will be a "sharper, more refined" (or words to that effect) version of what they have now, and not a "reality bender" (which he seemed to be implying maybe is coming, but not for a year or two).
FWIW, Sam Altman has fairly recently said that the jump from GPT-4 to GPT-5 will be similar to that from GPT-3 to GPT-4, and also (recent Lex Fridman interview) that their goal is explicitly NOT to have releases that are shocking - but rather they want to have ones of incremental capability to give society time to adapt. Could be misdirection - who knows.
Amodei for his part has said that what Anthropic will release in 2024 will be a "sharper, more refined" (or words to that effect) version of what they have now, and not a "reality bender" (which he seemed to be implying maybe is coming, but not for a year or two).