The lower limit of the input voltage of the error amplifier, the input bias current, and the inflow current of the COMP pin are different.
UCC2800: comp sink current 3.5mA (max)
UCC2813: comp sink current 2.5mA(max)

The Bode diagram is shown in Typical Characteristics Figure.1 of the data sheet, but UCC2800 has faster response speed.
UCC2800: 2MHz at gain margin 0dB
UCC2813: 1.5MHz at gain margin 0dB

Please refer to the URL of the datasheet below.
UCC2800: http://www.tij.co.jp/general/jp/docs/lit/getliterature.tsp?genericPartNumber=ucc2800&fileType=pdf
UCC2813: http://www.tij.co.jp/general/jp/docs/lit/getliterature.tsp?genericPartNumber=ucc2813-0&fileType=pdf