Sorry, but Brighton Park is definitely NOT similar to Woodlawn, not in architecture, not in ethnicity/demographics, and not in socioeconomics. Most of Woodlawn was built around the turn of the century (19th-20th). Brighton Park was largely built during the 1910s and 1920s. Woodlawn is overwhelmingly black. Brighton Park is overwhelmingly Hispanic (mostly of Mexican descent). Brighton Park is working-class/middle-class. Woodlawn is still quite impoverished though parts of it are slowly gentrifying.
As for similar neighborhoods, there's McKinley Park to the East, Archer Heights to the West, and Gage Park to the South. Due to gentrification, McKinley Park housing (whether rent or buy) will cost more than Brighton Park. Archer Heights costs around the same as Brighton Park. Gage Park costs less but has a higher crime rate.