Offer Allianz:
260,000 EUR - 20 years - 1.30% (repayment 2.45%) 812.50
120,000 EUR - 10 years - 0.45% plus 18,000 EUR grant (repayment 3.22%)
Outstanding debt after the end of the fixed interest period:
Allianz: 112,830 EUR
KFW: 65,675 EUR (grant already taken into account)
Offer HVB:
260,000 EUR - 20 years - 0.96% (repayment 2.5%)
120,000 EUR - 10 years - 0.75% plus 18,000 EUR grant (repayment 3.8%)
Outstanding debt after the end of the fixed interest period:
HVB: 118,054 EUR
KFW: 59,510 EUR (grant already taken into account)
I find the breakdown a bit strange. Based on your details regarding term, interest rate, and initial repayment, I calculated the following (without taking into account repayment-free years, etc.)
Allianz:
Installment 1: €812.50 Outstanding debt: €114,593
Installment 2: €367.00 Outstanding debt: €62,484
means a monthly burden in years 1-10 of ~€1,180 as well as a fictitious outstanding debt of €177,077
HVB:
Installment 1: €750 Outstanding debt: €116,743
Installment 2: €455 Outstanding debt: €54,661
means a monthly burden in years 1-10 of ~€1,205 as well as a fictitious outstanding debt of €171,404.
HVB has the lower outstanding debt; however, in years 1-10, €3,000 more repayment is made, which correspondingly has an effect. In years 11-20, HVB is at an advantage (without calculating in detail here), since the 20-year tranche is overall cheaper and the interest rate change risk after 10 years is lower for the KFW tranche because less outstanding debt remains there.
All in all, both are quite close. Intuitively, I would choose HVB; during my "bank tour," they were much more pleasant than Allianz.