The difference, if any, is in the noise. A far bigger factor is that between these two you are not attending a school with a significant presence in the top consulting firms so you probably won’t have (1) on-campus recruiting (2) alums in the firms that want to give people from their college a hand up. You can find lists of firms popular with consulting firms online, for example https://www.peakframeworks.com/post/consulting-target-schools
Your next summer is going to be critical. Your competition is not working at the mall, they are doing internships at impressive firms (often consulting firms) and will spin their experience for all it’s worth.
It’s worth adding that school name is not the entire story. Everyone who goes to Harvard and wants to work in consulting does not get an offer. Ability, personality, and plain luck play major roles. If you read the book “Liars Poker” you’ll recall that Lewis got his start thru a chance encounter at a banquet where he sat next to the wife of a managing partner.
Lastly, to the extent that pedigree matters to consulting firms another hurdle is that you are a xfer student. This can be a knock at some companies, especially if you are coming from a CC. Sure your diploma will only say UC but it’s easy for any company that cares to find out; they just ask candidates to bring a copy of their unofficial transcript to the interview or submit it when applying.
Consulting is a favorite topic on these boards. You can get more info by looking at older threads such as Tell me about consulting - #13 by CollegeMamb0