Is the FT232H a single channel version of the FT2232H?
The FT232H is the single channel version, the FT2232H is the dual-channel, and there is also an FT4232H quad channel part.

While these are all logically the same, with different numbers of UART channels, there are some performance and functional differences between them.


The FT232H has merely 1 kB of ring buffer, which can be overwhelmed if running at a high baud rate, and with a slow offtake by the host device. The FT2232H has 4 kB ring buffer per channel, much better in avoiding buffer overruns. 
Another difference, which may not be relevant to the task at hand, is that the FT2232H supports 16 GPIO pins via its internal 8051 emulation. There have been useful applications designed to leverage these GPIOs, but you may not need this. 


Keeping these two key deviations in mind, you need to evaluate whether your requirement is met by the single channel device. Often the buffer size constraint forces this choice to the dual channel part.

If price is not a blocker, a recommendation would be to stay with the dual channel part.