Although it is pretty obvious that helium balloons should be able to rise higher than hot air balloons due to much lower molecular weight of helium vs air, it could be still informative to look at how they rise and why they stop rising.
Both helium and hot air balloons rise because the lifting force, equal to the weight of air displaced by a balloon, exceeds the weight of the balloon (including the gas, helium or hot air, inside the balloon).
Both helium and hot air balloons stop rising because the density of air is decreasing with altitude and, with it, the lifting force. This is not the case with water, which has practically the same density at different depth levels and therefore keeps pushing objects less dense than water all the way up to the surface.
For helium balloons, this drop in density with altitude is partially compensated by the expansion of their volume, but still, at some altitude the weight will exceed the lifting force.
For hot air balloons the drop in density could be partially compensated by expelling more and more air, which could be achieved by raising the temperature in the balloon to progressively higher levels. But, again, at some point the weight of the balloon will exceed the lifting force.
So, even if the weight of the gas inside a balloon was zero, there would be a limit due to the finite weight of the balloon itself and the payload. This limit is lower for hot air balloons because they tend to weigh more and because, at any given pressure level, the density of helium will be lower than the density of hot air (for any practical temperature) and therefore helium balloons will have a greater lifting force for the same volume ($(\rho_{out}-\rho_{in})\times V$).
