I don’t think anyone has ever credibly asserted that San Francisco and Boston are peers much less that Boston is more significant globally.
Kmp -- your comment is really only pertinent when it comes to as a "venue for iconic entertainment"*
On all other important grounds Boston is in another league with True Top Tier Global Cities
*1
Action Movies:
SF: Dirty Harry Series, Bullet, The Rock, the Presidio, View to a Kill
BOS: the Friends of Eddie Coyle, The Brinks Job, The Town, Tomas Crowne Affair, The Departed, Blown Away, Shutter Island, Black Mass
Edge SF because of the stars and the chase scenes on the hills
Popular Music with City in the Name:
SF: I left My Heart in San Francisco
BOS: Shipping Up to Boston, "Love that Dirty Water Boston your my home" [honorable mention]
Big Edge SF
Classical Musical Organizations:
SF: SF Symphony
BOS: BSO, Boston Early Music Festival, Handel & Haydn Society
No Contest: BOS by knockout
Art Museums:
SF: San Francisco Museum of Modern Art (SFMOMA), Legion of Honor & de Young Museum, Asian Art Museum, San Francisco Camerawork
BOS: MFA, Gardner, ICA, Fogg
Huge edge BOS
Sports Teams::
SF: Golden State Warriors, San Jose Sharks, San Jose Earthquakes [soccer] SF Giants, SF 49ers, Oakland Athletics, Oakland Raiders [gone]
BOS: Red Sox, Patriots, Celtics, Bruins, Revolution
Split decision to BOS: SF has one more team, BOS has teams with unchallengeable history, both cities depend on remote teams to fill out the roster
Iconic Sports Venues:
SF: Levi's Stadium [football], Oracle Park [baseball], Oakland Coliseum [ostensibly baseball], Earthquakes Stadium [soccer], Chase Center [basketball] SAP Center [hockey]
BOS: TD Garden, Fenway Park, Gillette Stadium
Split decision: to BOS -- SF and environs have more facilities though some a way out but BOS has the iconic Garden and Fenway with honorable mention to Gillette and then BOS has all those championships
Iconic Infrastructure:
SF: Golden Gate and Bay Bridges
BOS: Big Dig
edge SF