I'm strongly in favor of giving the parliament the ability to propose laws (directives). Currently only the comission can do that.
The way it seems to work in practice (here at least) is most partisan/normative legislation goes through the lower house upwards
And bipartisan (or broadly unpopular or highly technical) legislation goes from the upper house down
It’s more complicated than that, but a one way flow committee sounds extremely restrictive for meaningful reform
A small number of pathways is a good thing, one lone process is probably not (you risk over fitting on both sides)
Edit: Australian legislation has a lot of flaws, but this multimodal setup from my experience is not one of them
education seems similarly harmonized in both unions (the Bologna system works pretty well)
but just as in the US border issues are always affecting members differently (migration flows North, right? so southern borders are affected more; at the same time migrants went to NYC and Berlin because they are rich cities with opportunities and very migration-friendly policies)
and of course federalism in the US is also suffering from vetocracy (aka. tragedy of the anticommons), see housing, which very directly leads to "blue states" losing seats in the House (and similarly housing issues are catalyzing radicalization in the EU too)
(and the solution to the housing challenges are not obvious, and even if there are success stories - like Vienna - city-state politics is stuck in the usual local minimas)