The virus that causes COVID-19, SARS-CoV-2, is phylogenetically most closely related to SARS-CoV, the virus that causes SARS- this is why taxonomists named it SARS-CoV-2.
However, you shouldn't and can't expect SARS-CoV and SARS-CoV-2 to have a more similar course because of this, as compared to MERS-CoV- and in fact thus far they've behaved differently. For instance, the death rate for COVID-19 is considerably lower than for SARS. Paradoxically, this may be responsible for its greater spread, because people who are less severely ill or asymptomatic are much more able to spread disease widely or in an undetected fashion. In the US there has been undetected community spread of SARS-CoV-2.
I don't think it's useful to use epidemiological properties of other related strains at present; the data we have directly about SARS-CoV-2 is already superior to extrapolating this way. COVID-19 has already expanded far more geographically than SARS ever did, which already makes the overall probability of extinction of it less likely than with SARS, as generally speaking extinction probability decreases with increasing population size.