Is there a big difference between Columbia SIPA and Harvard Kennedy?

[leftist_policy_wonk]

About me:

• M26, software engineer with 3-4 years of experience, Looking to career pivot into public policy
• Politically on the left: have volunteered for campaigns that align with the Zohran, AOC, Bernie camp. Am a DSA member.  
• Fields of policy I'd love to make an impact in: tech anti-trust/AI regulation, labor policy, immigration policy, and gender equality. I know less about international policy, although I've found it increasingly interesting over the last few years, so I wouldn't say no to it
• Currently live in NYC and my friends are all here and would love to stay, but I don't wanna kick myself 10 years later because I didn't want to sacrifice 2 years of NYC
• I'm a dancer outside of work, which is part of why NYC has been great since there's been a lot of opportunities for that

Offers & Scholarship:

• NYU Law - no scholarship yet
• Penn Law - no scholarship yet
• HKS - $30k a year (Remaining tuition: $42k a year)
• Columbia SIPA - $55k a year (Remaining tuition: $28.5k a year)
• UChicago Harris - $35k a year (Remaining tuition: $38k a year)
  • Submitted scholarship reconsideration as well
• UC Berkeley Goldman - $15k a year (Remaining tuition: $19k a year) (in-state)
• Georgetown - $17k a year (Remaining tuition: $41k a year)

Questions:

• HKS is the best program, but I hear it is still difficult to get a job afterwards. How big of a difference is HKS and SIPA?
• I have an undergrad degree in CS and want to work in tech/anti-trust/labor policy (open to any progressive policy goals though). So I applied to JD programs as well for JD-advantaged jobs. Would a JD from NYU Law give me a better foot into the door of these jobs than an HKS degree? It's expensive of course, but if it's worth it, I can look into external funding/scholarships.