In your 1st comment you didn't state Macro algae, you just stated algae.
Bryopsis grows considerably faster that cheato .....
Not sure if it out grows it or not, but sea lettuce grows pretty quick....
Bryopsis doesnt grow that fast. Bryopsis is stubborn in that it can pull nutrients out of the rock its growing on, and can also use trapped detritus inside it as a source of nutrients, but it doesnt grow particularly fast.
If bryopsis grew faster than chaeto, it would used as a nutrient export algae instead of chaeto, or calerpa. The purpose of using algae as a nutrient export device is to strip out nutrients that algae uses to survive. This is done by using a fast growing algae, (preferably the fastest growing available), which out competes other algaes (such as bryopsis), by growing faster than the other nuisance algaes. It's impossible to outcompete anything (population wise), by reproducing slower than your competition.
As long as you have decent lighting, a photo period of 18 hours or less, and magnesium is under 1500 ppm, chaeto will grow in your system. It will grow faster if tumbled or exposed to light from all directions.
The only other macro algae which grows at a similar rate in the aquarium is calerpa, and there are significant disadvantages to using it for nutrient export.
Ulva is what is commonly referred to as sea lettuce. It does not grow as quickly as chaeto or calerpa. All of the ulva I saw in the wild was growing in high surge zones where chaeto and calerpa could not survive. Additionally, neither chaeto nor calerpa were endemic to those areas...