So the major, common and probably most destructive, theme is the ecosystem of specialised tender companies. I mostly know this from the software side, but if you start working on such projects, you'll quicky find out that there's a persistent ecosystem of companies which specialize for these tender signups.
People employed there optimize for winning them (at any cost - quid-pro-quo agreements aren't rare in my experience). It's common for several such companies to collude in a way that they get awarded the tenders in a circle ("I get this one, next one is for you.")
Afterwards, they outsource the work to the cheapest lowest bidder (usually IT studends in the cases I've seen for software development, but essentially they'll be bottom of the barrel juniors). The quality of such products is about the same as the quality of any outsourced product which is built only to satisfy a checklist at the end. The US equivalent of that would be a corporation getting a defense contract and then basically have everything built by the cheapest outsourcer in India or similar location.
Funny enough, university labs (or spinoffs) tend to be major part of this ecosystem, using grad students as workforce - their credentials tend to give them legitimacy over smaller companies.
The results are as disastrous as you can expect - companies a HNer could expect to win usually don't (due to lack of specialized knowledge on how to game the tender process, lack of connections and cost) and those that do are really there to do the bare minimum, shed the work as much as possible and deliver something they can't get sued over.
It's also not uncommon to see whole chains of such companies - the winner sometimes shares some outsourcing work with "losers" they outsource work further, skimming the funds on top and essentially outsourcing everything to the cheapest engineer they can find.
Dealing with any public EU project has been nothing but misery for me personally (as you can imagine from this post :) and this environment bred some of the most toxic workplaces I've worked with. The products were universally terrible and rarely actually useful for the purpose.
As much as I want independent EU software ecosystem, I don't think using public funding can breed anything but more corruption.