Decent school with a mediocre GPA, No-name school with an excellent GPA, who is the better candidate?

I know GPA is an essential element in postgrad applications, I'm just wondering if there are two candidates, one is from a prestigious uni but with a mediocre GPA and the other one from a no-name school but has an excellent GPA, which one is professors prefer?

Specifically, now I'm choosing where to take my bachelor's and I have two choices (Bocconi and Waseda), which I posted before. I've heard of the competition at Bocconi is fierce and you can hardly get a GPA higher than 28/30 (converts to final grade 106/110), especially for non-italian. In Waseda, I can easily get an A/A+ and there is nearly no competition.

My final goal is to take an Econ/Stats PhD in the U.K(Oxbridge), and their lowest requirement for Italian applicants is 106/110.

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Prospect in PE - Other

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Perspective from a Brit (LSE/Imperial/UCL UG, Oxbridge PG):

You're thinking about this wrong - the most important thing for PhD admissions is evidence of research potential. For econ, this will likely include published papers and exceptional references.
I've never heard of Waseda but it does - from a quick Google search - appear to have a decent reputation/output. However, Bocconi will be very well-known in the UK and there'll be a lot of cross-pollination between Bocconi and top UK research groups, so adcomms may know your references which will always help.
That said, grades > institution by far in general - mostly because your references will be much better.
But the grades only matter so much - once you meet the broad qualifications (equivalent of a First or 3.7/4.0 GPA if you want to do a PhD at Oxbridge, the top three London unis, or Warwick), your references and research potential are far, far more important. This is slightly different to the US as people are generally admitted to the UK out of master's degrees and don't undertake much, if any, taught coursework in their PhDs.
Depending on the programme and how funding is set up, you may need a strong "pull" factor - i.e. you have someone on the university side who actively wants to work with you. Network well in advance.
For econ, you're much better off going to LSE over Oxbridge in my opinion. For stats, there's a strong argument to say Imperial over Oxbridge too - and depending on your research interests, do strongly consider Warwick and UCL. Do not choose a PhD based on your institution, choose them based on your research groups - econ/stats is quite broad.
Econ programmes in the UK are pretty poor compared to the top US programmes - even LSE's placement is much worse than peer US institutions now (didn't used to be the case), and you will struggle to get a post-doc position at a top US university unless you're top of the cohort or doing something exceptionally relevant to their research groups. But for European academia, corporate gigs, and IGOs (LSE and Oxford place very well), you'll be fine.
In answer to your original question, I think I would go Bocconi here just because it's a much lower risk option. As long as you can finish in the top 20% or so you'll be alright, and focus on building good recommendations for research potential over being in the top 5%.
EDIT: Just saw your posting history and that you're a HS student - when I was writing this I thought you were applying for an MSc for some reason at these two universities before looking to do a PhD afterwards. As you'll probably have to do a master's before being admitted to a PhD, just do Boconni and don't look back. Don't stress about being top of the class as you'll probably go elsewhere prior to the PhD; then focus on getting exceptional references during your master's programme.

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Appreciate for your advices, really helpful, but I still have some concerns as follows：

As U.K has a strict requirement to applicant's GPA, once if my GPA is under 106/110 at Bocconi, I will be put in danger. I guess the PhD programs in U.S have a more flexible requirement to applicant's GPA and more diversity recruit. While I'm not passionate about academia and be hopeful to get a quant job after my PhD, do you think PhD programs in U.S is still a better choice because their flexible requirements?
Yes, I think most of professors in the West are not familiar with the levels of Japanese universities (except for UTokyo), so they just search those universities' name as same as others. From this perspective, Waseda is definitely not totally unknown, so do you think professors will be willing to recruite a student from there with top grades since every school has their own good students?
Bocconi is really hard, 5% or even 20% is unrealistic for me I think, objectively. Thus, it's highly probable that I will fall down to lower than 30%, which hurts my GPA and rankings. Honestly, based on my observation, there are not many internationals get top grades.
Also, publishing papers at undergraduate level is nearly impossible for econ majors / Bocconi has a top-down teaching system as similar as LSE, and only graduate students can do some research projects with those famous professors at IGIER (their research center), so recommendation letters might be not very detailed and convincing.
Overall, the final situation is very likely be among Waseda applicant with a 3.8/4.0 GPA vs Bocconi applicant with 105/110 (equivalent to U.K 2.2 i guess)

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5y

A few points:

If you're interested in corporate quant gigs, a master's (especially from Oxbridge/Imperial - less so LSE) will often be enough. These jobs are incredibly competitive, however, and most people are coming in from a maths/physics/computing background not econ.
Providing you can get funding, UK PhD probably makes more sense for your ambitions as it takes less time.
If you want to actually be competitive for direct PhD entrance to Oxbridge/LSE/Imperial/UCL/Warwick, you really need published (at least co-author) papers. Either that or you're truly exceptional as an interdisciplinary leader (Rhodes, Marshall, Schwarzman level) and you'll make a difference outside of academia. This is why predocs in the US are becoming increasingly common. Many of the top UK unis, as a matter of fact, do offer tonnes of research opportunities for UGs (would highlight LSE and Imperial in particular).
You will almost certainly need to do a separate master's before being admitted directly into a PhD programme. One way to avoid the funding problems with this is to apply for a joint four-year programme (MPhil-DPhil or MRes-PhD). These are immensely competitive though and you will need, at the very least, good research experience with exceptional references (even if your work itself is unpublished).
I don't know about the Italian grading system, but I highly doubt the top students at Bocconi are not competitive for the top UK programmes. Check LinkedIn for former Bocconi kids now at top UK PhD research groups and ask them about the grading.
If you think you can't get top 30% at Bocconi, then I'm sorry to break this to you but you're kidding yourself if you think you'll get into a econ or quant PhD programme at a top six (yet alone Oxbridge) UK university. Be realistic about your ambitions. You basically need to be top 30% at one of the six UK universities I've mentioned to get into most decent taught master's programmes at Oxbridge/Imperial/LSE, or top 5-10% if you're coming from the UK equivalent of somewhere like Waheda (lower Russel Group?). And research master's are more competitive than taught ones and will be prioritising your research potential.
Similarly, the people doing quant jobs at HFs are generally the best people in their programmes at the best universities. Honestly speaking, it sounds like you don't think that you're at that level. Now, that may change throughout UG as you mature, but I would urge caution in your case of planning UG > direct admittance to econ/stats PhD at Oxbridge > quant HF as an incoming UG student. The only people (and there will be people like this at Bocconi) who should really be considering that as a viable option at your age are the people who topped their subject nationally or globally in their school leaving exams, international olympiad competitors, etc. Others will develop their potential as their degree progresses, but you're shooting yourself in the foot here by trying to plan your postgraduate career now.

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Decent school with a mediocre GPA, No-name school with an excellent GPA, who is the better candidate?

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