Number Seven Boat Trips and Bristol Ferry Boats both operate services in the city's harbour. Number Seven Boat Trips said the changes were "unjust".
Bristol Ferry Boats disagreed and said the new timetable was "fairer than the previous one".
The city council said it was introduced "following feedback from customers".
Both companies operate the same route between Temple Meads and Hotwells, at staggered times.
Previously, the two boats collected people every 10 minutes in a 20 minute slot - and then one boat picked up passengers over the next 40 minutes.
Changes now mean ferries collect at regular 20-minute intervals and passengers can now stay on the same boat for the whole trip, instead of changing in the city centre.
Richard Rankin, of Number Seven Boat Trips, said: "We're told to move from our timetable on the Hotwells route - which we've run for 15 years - 10 minutes earlier.
"What it does then is, by running two boats close together it maximises the potential for what passengers there are to get on the other side's boats.
"That strikes me as being very unjust."
But Philippa Bungard, from Bristol Ferry Boats, said feedback indicated the service was "better for everybody".
"[It] is much fairer than the previous timetable and everyone so far seems very happy," she added.
In a statement, the council said the changes were made to manage journeys in the "most effective way".
"The changes have been made following feedback from customers using the services, to ensure timings between the two do not overlap and deliver the best experience for visitors," they explained.
A ferry boat firm in Bristol is claiming a new timetable "imposed" by the council favours its rival.