I can't answer as to how the interface acts with doing multiple pictures, being clunky, etc. But there is one aspect that I'm not sure if you know (jlandry definitely doesn't). With your iPhone, if you were on wifi and sending to another iPhone, it didn't actually go through MMS (multimedia messaging service), it went through iMessages. So depending on how good your data signal is on the S4, it might have been faster over wifi. Even just comparing on data signal on both phones, the MMS protocol is old and (IMO) clunky. So I would think it's going to upload slower than the iMessages protocol.
MMS cannot go through wifi, so being on it versus not won't make any difference, jlandry. Though some Android phones have a problem of switching over while connected to wifi and sending an MMS. And they will just stay on "sending" until you turn off wifi or leave the wifi area. But that is just a software bug, and doesn't mean that wifi can handle the MMS protocol.