By default (as of 24 Nov 2023, Mathematica 13.3), it appears that ImageSynthesize uses Dall-E-2 for image generation, as the results are kind of trash—but with some tricks you can get it to use Dall-E-3 instead…:

Here’s an example using the default settings:

ImageSynthesize["A cartoon of a a capybara riding a motorcycle and wearing a bowtie"]

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ImageSynthesize does not appear to accept LLMEvaluator option (like LLMSynthesize, etc. does):

ImageSynthesize["A cartoon of a a capybara riding a motorcycle and wearing a bowtie", 
  LLMEvaluator -> LLMConfiguration[<|"Model" -> "dall-e-3"|>]]

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It looks like by default the OpenAI Service also uses Dall-E-2 (although I am not sure why it throws this error):

ServiceExecute["OpenAI", "ImageCreate", {"Prompt" -> "A cartoon of a a capybara riding a motorcycle and wearing a bowtie"}]

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However, there is an (undocumented) model specification ability to specify models. Notice how Dall-E-3 better captures the characteristic nose shape:

ServiceExecute["OpenAI", "ImageCreate", {"Prompt" -> "A cartoon of a a capybara riding a motorcycle and wearing a bowtie", "Model" -> "dall-e-3"}]

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Confirm that the default versions use Dall-E-2:

ServiceExecute["OpenAI", "ImageCreate", {"Prompt" -> "A cartoon of a a capybara riding a motorcycle and wearing a bowtie", "Model" -> "dall-e-2"}]

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ToJekyll["Dall-E-3 image generation in Mathematica", "mathematica openai chiguiro art"]

Parerga and Paralipomena

Came across some recent Wolfram Community posts that provide relevant functionality: