I would check that plumbing and linkage between those carbs. It sounds like the second carb is starving for fuel as the accelerator is advanced.
The carbs combined use about the same amount of fuel as a single carb.With about 1/2 the fuel going to each you would not see a noticable differance in performance until you exceeded the low idle or slow driving stage.
As you depress the accelerator the carbs call for fuel as the floats drop in relation to the amount of fuel you are dumping.
A common problem is a blockage between the carbs sometimes but not always related to a "softened rubber hose" that will close off as it gets hot.
A second common problem is improper linkage adjustment between the two carbs.One dual carb configuration is of the progessive type where the second carb is not dumping fuel at the same rate and time as the first carb but increases as the demand is put on it.If this is the setup you have you might need to change the linkage so that both carbs are dumping simultaneously.
Another possible problem is a malfuctioning choke.It could be that the choke is being closed from iterference of a linkage rod or other cause.Just another area I would check.
Hobert
