No reason to believe it's any more secure. However, if you are actually in an SSL (https) session you are as secure as you're going to get. The only real way to hack that would be if someone was doing a man in the middle attack and pretending to be your bank (or whatever). Even then there would be a certificate mismatch. But I still agree with your second paragraph, don't do anything important on a public network if you can avoid it.
"Good judgment comes from experience. Experience comes from bad judgement." - Will Rogers
DW and I - FIREd at 50 (7/06), living off assets