I'm not sure "rather" is the right word here, but the early studies showed dry cough as a more frequent correlate of Covid-19 positive PCR tests compared to wet cough, according to WebMD:
Early studies have found that at least 60% of people with COVID-19 have a dry cough. About a third have a cough with mucus, called a “wet” or “productive” cough.
(Someone can perhaps dig up those studies, WebMD doesn't link to them.)
The Guardian likewise noted
According to the WHO, the most common symptoms of Covid-19 are fever, tiredness and a dry cough. Some patients may also have a runny nose, sore throat, nasal congestion and aches and pains or diarrhoea. Some people report losing their sense of taste and/or smell.
(Emphasis mine.) That doesn't mean there aren't less common symptoms, although admittedly the mass media usually doesn't seem to mention those less common ones.
Healthline posted this interview with an expert, which hopefully is correct with respect to the timing of the cough type relative to Covid-19 progression:
Dr. Bruce E. Hirsch, attending physician and assistant professor in the Infectious Disease Division of Northwell Health in New York, said there is some overlap between COVID-19 and other diseases caused by viral infections.
“Differences between coronavirus and influenza and more common viruses still in circulation are that we know that the coronavirus binds to receptors in the lower part of the airways, and that accounts for the fact that so frequently, but not always, dry cough along with fever and fatigue are three of the symptoms that are most commonly associated with COVID-19,” Hirsch told Healthline.
While dry cough, fever, and fatigue can occur with other viral infections, he said muscle aches and pains are distinct signs of the flu, while the common cold may bring on with a runny nose, sore throat, or sneezing.
“Having a runny nose is not expected with COVID-19 infection. Having muscle aches and pains is much more common with influenza. Having a productive cough, coughing up phlegm, can occur with COVID-19 infections, particularly late on, but it’s not typical with what the early course is,” said Hirsch.
Although again, no detailed studies are liked/mentioned.