Career advice: Transitioning from LatAm Early Stage VC to US LMM PE?

Hi all, I'm currently a senior analyst at an early-stage, generalist VC fund (sub-$35M) in LatAm. I've been with the firm for 2.5 years and have either led or played a significant role in most of the investments we've made. I recently received an offer to join a LMM PE fund in Houston that focuses on the industrials and energy infrastructure sectors. The firm has been around for 3 years and I would be their first external hire. The partners, especially the operating partners, are quite impressive—one of them previously worked as an infrastructure advisor at a MF (BX/KKR/Carlyle/TPG) after selling his company to them. Also they've had 3 exits so far all with 2-3x returns. For additional context, I currently live in a country with no investment banks or PE funds, and the VC fund I work at is the first in the region and the only one in the country. Hence, this opportunity is quite rare for someone with my background, even though it's not at an UMM or even a MM fund and would represent a significant pay raise. For added context, I'm interested in pursuing an MBA at a top school in the US. After speaking with a former associate at the fund who was admitted to Sloan, he believes that staying at the VC fund to finish the investment period and help fundraise for the next one might give a more compelling story. However, he also sees the value in transitioning to PE to acquire the technical skill set to potentially try and transition into GE in the future. If you were in my shoes, would you stay at the VC fund, or would you work in PE for 1-2 years to gain the skill set and increase your options? Thank you for your advice.

Edit: I’m also applying to LSE’s MFin but I haven’t received an answer from them. So another thing I wanted to ask is if I should wait for an answer and forgo the PE opportunity or take the offer and apply next year after learning for a year.