It’s worth highlighting that both Bard and ChatGPT sit on models (LaMDA and GPT-3.5 respectively) that sit on Transformer-based deep-learning neural networks.
Google Bard is produced and owned wholly by Google, on top of LaMDA, which is also created by Google. ChatGPT is developed by OpenAI, a San Francisco-based AI research lab. OpenAI was originally nonprofit but it did create a for-profit subsidiary back in 2019.
They’re designed for different purposes, too. Bard will help you navigate Google search. It’s designed to be conversational. ChatGPT can generate entire blog posts. It’s designed to spit out chunks of text that make sense.
It’s hard to give a fair answer to this question because they’re both so similar, yet so different. For one, almost nobody can access Google Bard right now. For another, ChatGPT’s training data were cut off almost two years ago.