Personally I'd rather rebuild the old carb than replace it with a cheap new one. Some of those are not all that good. Most OEM carbs are better quality.
Why did you replace the carb in the first place? If it was due to the same symptoms you're seeing now, then clearly the carb is not the problem. It could be a fuel flow problem. One possible cause of poor fuel flow is a clogged tank vent. That is usually in the gas cap. If air can't flow in to replace the fuel that's being used, it will slow fuel flow.
The usual way to check fuel flow is to remove the fuel line from the carb and let it run into a container for a set time then measure the flow. But you need to know the factory flow rate for that. Who manufactures the engine? If it's Kohler or Honda, they are pretty good about supplying extensive data in their shop manuals and they may have a spec for fuel flow.
Another possibility, especially if the engine was running to full rpms before the carb swap, is that the carb linkage is assembled wrong. And if it's a cheap aftermarket carb it might just be defective.