I am (regardless of my "sector bias") not a fan of generalizing statements.
I know local banks that match every online condition and I know local banks that do not do that on principle.
Things like risk costs or option costs are essentially the same everywhere because all banks (whether local, global, or internet-based) basically operate in the same market.
There are banks (yes, also savings banks) where you put together the conditions yourself if you want extra prepayments or this or that.
By the way, I also know many providers who offer both 3 months BHZ or 12 months BHZ equally well, only one interest rate is 0.05% higher.
And then there are even savings banks that have included various things in the interest rate, starting with 12 months BHZ, a flat-rate 10,000 EUR prepayment, appliance protection for 5 years, 10% refinancing reserve (without mortgage!), etc.
So, however you look at it. I am very neutral here, especially since I am not a salesperson.