Advantage of having a Green Card while applying for PhD?

[pillowsopher]

Hi everyone,

My partner is in line to get a Green Card, and I'll be eligible to apply for it once she gets it. I plan on applying for PhD programs in the US as an international applicant, but I wanted to know if it would be better for me to apply as a permanent resident instead. Based on the information available online, it looks like the latter is helpful in reducing the fees, but I guess that's more important for Undergraduate and Master's programs rather than than a PhD. Are there some clear advantages to applying for a PhD as a permanent resident instead of as an international applicant?