The code does the same thing: Integrate the conductivity matrix and the heat load.
The deal.ii code on the right is in C++. The Julia is I think easier to read, and, at least in my test, it runs (slightly) faster.
EDIT: Second measurement: deal.ii code is ~6% faster. Not sure why the first measurement indicated the opposite. Sorry about the misinformation.
EDIT: Third measurement on a laptop with no load other than the calculation: codes run at the same speed.