I'm trying to compare the connection security of two different websites. I'm going to be entering some Sensitive personal information into one of these websites, and, because I'm not familiar with this part of the banking world, I'm looking for some opinions on their security. I've checked the Connection Security on both websites and one seems a bit "behind the times". I'm also not an expert on this aspect of Information Security, but I have a general understanding.
Website A: TLS 1.0 AES with 256 bit encryption (High); DH with 1024 bit exchange
Website B: TLS 1.2 AES with 256 bit encryption (High); RSA with 2048 bit exchange.
Website B seems more secure because its using TLS 1.2, though my understanding is the security also has to do with implementation. I am also more familiar with RSA vs "DH" though I won't pretend to be an expert. I also don't want to fall for the fallacy of "bigger numbers = better". Website B is also part of a major credit agency so I feel more comfortable with them.
Thank you for any help you can provide!
EDIT: I ran both sites in ssllabs.com as suggested by user kaidentity. Site A got a C- and Site B got an A-. I'm still interested in hearing (and learning) more if anyone has anything else to add.