I sort of had similar problems but with my iPhone s4. Constant sim problems. Was working great in the Nexus4 but not in the iPhone.
I ended up asking them for a new sim and the problem went away.
This might not have anything to do related to your problems but sometimes it might not be the phone itself.
Are you using an Sim adapter with the Nexus 4? The Nexus 4 uses a MicroSim and the iPhone5 a NanoSim and since you didn't have problems swapping between the iPhone4s and Gnex I would think it might have something to do with it.
I ended up asking them for a new sim and the problem went away.
This might not have anything to do related to your problems but sometimes it might not be the phone itself.
Are you using an Sim adapter with the Nexus 4? The Nexus 4 uses a MicroSim and the iPhone5 a NanoSim and since you didn't have problems swapping between the iPhone4s and Gnex I would think it might have something to do with it.
I'm a Nexus 4 and iPhone 5 user. I love both phones, but I'm having issues with my Nexus 4. I would use my iPhone 5's sim which is a AT&T LTE SIM card in my Nexus 4. Right out of the box I had to change the APN settings to get the data and MMS working properly. Once I got text and data to work, I wasn't able to send or receive a text with a picture. It would just say sending. While I was going to make the exception, the bars would go grey. It show'd full bars but I couldn't get data. Calls only. Like the radio was disabled. I knew if I was to go to AT&T and let them know, they would most likely want to change my data or switch to a non-iPhone data plan. I'm very frustrated and want to use my Nexus 4, but I guess I'm having to go back to my iPhone 5 for now. I had the galaxy nexus and switched my sim from my iPhone 4S to the GNex all the time and had no problem. I don't know the deal. If anyone has the same issue, I would like you to chime in.