Currently I use a power supply
"super flower 450p14p"
Combined power (+12 V) 444 W
Max output power (+12 V) 37 A
Or should I rather change to this power supply?
"Thermaltake Berlin 630 W"
Combined power (+12 V) 540 W
Max output (+12 V) 45 A
what can happen in worst case, if I try the weaker power supply?
Thanks for your help
Worse case scenario? Well let's assume you're overclocking, and it has OCP (over current protection), it may just shut off. Let's assume it doesn't shutoff and has OTP (over temperature protection). An overclocked S1 will likely pull ~99% of the available current. It will probably then overheat and.... shut off. Of course it could have none of these protections and just burn out/catch on fire.
Let's assume that OCP and OTP aren't triggered and it's pulling 99% of the availble +12V power. It's highly likely that the PSU is group regulated, so by loading the +12V rail all the way the voltage will drop (probably below 11.9V) which will cause the S1 to have massive hardware errors.
If you're not overclocking the S1, it'll probably work fine.
On the otherhand, the thermaltake will likely not really suffer from any these issues and work like it should saving you grief, headache, and stress.