Here's an example using the case of €30k borrowed over 3 years @7.5%
Monthly payment - €933.19
Over 3 years, the loan would cost about €3600 in interest meaning you would need about 4% return p.a. before you recoup these costs.
All returns below would be before taxes, fees, etc.
Scenario A
Investing the €30k from the offset will leave you with the following amounts after 3 years (assuming continuously componded interest)
@3% annual return - €32,835
@4% annual return - €33,825
@6% annual return - €35,916
@8% annual return - €38,137
@10% annual return - €40,496
Scenario B
Investing the same €933.19 on a monthly basis (i.e. taking on no debt) for three years at the same rates of return as Scenario A will yield you the following:
@3% annual return - €35,197
@4% annual return - €35,753
@6% annual return - €36,900
@8% annual return - €38,095
@10% annual return - €39,341
So, at low-medium (realistic?) rates of return, you are not at all compensated for the risk of borrowing €30k when compared to a regular, monthly investment. Even at 10% annual return, you will see just €1000 extra in return for your risk. Maybe others can clarify whether having €30k to invest from the get-go would allow a greater chance of achieving higher returns....
The only thing I can think of is that fees and other charges for whatever you invest in could be an issue when paying regular monthly increments. This could be offset by the fact that you will pay less tax in Scenario B (investment is approx. €933 x 36 = €33,595) than Scenario A (taxed on everything above €30,000)