In many cases, it should be able to replace your film. If you need high sensitivity, you will want to use a substrate that has higher reactivity and is designed for digital imaging, such as SuperSignal West Dura, Femto, or WesternSure PREMIUM. In most cases, these substrates will get you what you need.
I only have experience with the Odyssey scanners. Based on the C-Digit specs the scanner looks inferior to those so I would say not as sensitive. If you have the budget I highly recommend the Odyssey. In my hands the sensitivity is as good or better than film and because you can multiplex the cost per blot is significantly less than film.
Thank you for all your comments. In the meantime I had time to test a C-digit machine. Two westerns were prepared under exactly the same conditions with a 1:2 dilution series of a flag-tagged protein. After developing with Western SURE premium substrate one was exposed 5minutes to GE ECL film, the other one was read with the C-digit. The C-digit could read 4 dilution steps, on film 5 were visible. In essence the C-digit will be able to cover about 80% of my western needs, saving multiple exposures and allowing for direct digitalization. I agree with Thorsten: A nice gadget where it is appropriate. Nice to have but one needs to have the money....