You are unspecific about which shields that you are using - not to mention which Arduino. For all that, about the worst thing you might be faced with is that both shields rely exclusively in the 6-pin ICSP cluster for the SPI bus, thereby obliging you to replace one socket with one that has extension pins.
Check the specifications.
I have never seen an Ethernet shield with wiring options, but the host shield should be configurable. If it isn't, get one that is.