The way I understand it is this:
The CDMA LTE side will only work with Verizon. Not with any other CDMA carrier like Sprint or US Cellular.
The GSM side of the VZW iphone will work internationally on many LTE bands. Domestically, due to the 700 mHz FCC laws, it cannot be carrier locked. This means that domestically it can be used with at&t, tmobile, straightalk, aio, etc.. However - just because it can work with them does not mean it has to work on their LTE bands.
For example - If I put my wife's at&t iPhone 5 sim card into my VZW iphone 5, it works but only on their HSPA+ network. Not on their LTE. Same thing for my iPad. I have a Verizon 4th Gen. It works LTE with a verizon SIM but only "4G" HSPA with an at&t SIM.
I beleive it will be the same for the 5S. The difference is that internationally, you will have more options for LTE.
Again, this is just my understanding. If I am wrong, please feel free to correct me. Politely (something grossly missing on this website)