I believe their communication layers are fairly different – WhatsApp used to use something based on XMPP at least until a while ago; I'm not sure what Signal uses, but I vaguely remember it being based on HTTP?
Can definitely be, I never investigated in detail, although I used alternative open source clients for both (signal-cli and a long time ago yowsup), so the information should be in there...
I hoped that Signal's use of HTTP was as a fallback in case a direct connection could not be established to use a more "compact" protocol, but I possibly don't remember correctly what I've read...
