This is patently false. To address a couple of points: if you have a subsidized student loan, you will not accrue interest in grad school. If the loan is unsubsidized or a private loan, interest accrues always. Most master’s degrees and professional doctoral programs are unfunded, so students will take out loans and accrue student debt. Some PhD programs are fully funded, but even that stipend tapers by year six and year seven (which is normal in the humanities, less so in the sciences) and many will take out loans.
As a Duke junior who also went to a directional state school for a while, the level of critical engagment, reading load, intellectual complexity is higher at Duke than it may consistently be at ASU (because not all of your courses, I’m assuming, will be in the Honor’s College). The level of networking, if that’s important to you, is probably higher at Duke, though ASU will concentrate its resources in Barrett, so it may end up being the same. Research opportunities are broader at Duke-- but more students will also be competing for those research spots. At ASU-Barrett, you may have to put in more work contacting professors/creating research opportunities, but there may be slightly fewer students competing for those spots.
To be honest, Duke (and I presume many similar schools like us) is also a pressure-cooker, so that’s something to consider. ASU will probably have a different feel (even when you’re within the honors college), as it’s a large state flagship, and even with our sports, Duke is a private R1.
The $128k is not just change, and I would consider what that money is worth to you. Look into how FA works for summers and study abroad. Could you afford to study abroad over a semester or summer while at Duke? Participate in institutes/other programs that may cost money?
Depending on the kind of grad school you’re going to, you may need that money for grad school. If you’re looking for a straight PhD in Chem/Biotech/etc., that may be funded. If you’re looking for a master’s in Chem/Biotech/whatnot to work in industry, that may be funded by your company, but are also many times self-funded.