Does the interface affect the sound of a recording? Sure it does. There is an audible difference between a high quality interface and a cheap one. My Lynx Aurora interface sounds much better than the Aardvark Q10 I started out with. At the Lamda - M-Box level, though, it is unlikely that there is much difference. These are essentially both at the same price and quality point.
In the scheme of things, though, room treatment and better microphones and preamps will usually make a more distinctly audible difference in your recorded sound than your converters.