Stick to current MM or move to established upper-end MM?

I'm currently interning at a European mid-market PE firm that's (relatively) unknown outside of domestic borders.

A significantly larger and more established EU firm (think Cinven, Advent, 3i) has recently set up shop in my city and extended me a conditional offer upon finishing my current internship.

I have also been offered to stay longer at my current shop. I'm in doubt about which option would be best since the work I am currently doing is very rewarding and broad (i.e. from being involved with portfolio companies to working on a live deal), and I am afraid that the work I'll be doing at the larger fund will not be (mostly sourcing, administrative duties, etc).

Keeping other factors such as pay out of the question, would you guys argue the brand name is worth the trade-off?

Thanks