Faux wood blinds and cellular shades are both generally less expensive than wood blinds, woven wood blinds and many Roman shades. Faux wood tends to be a little less expensive than cellular shades.
Privacy and the View
Faux wood blinds can be opened a crack to let in light (and even part of the view) over the whole window. Cellular shades can be opened only from the bottom or top. When fully closed, blinds tend to darken more, while shades tend to let in more light.
Cellular shades offer significant insulating capacity--so much so that some shades are eligible for the federal tax credit for energy efficiency. Faux wood blinds can't compete there.
Ease of Cleaning
Faux wood blinds are significantly easier to clean than cellular shades and are more durable for the long term.
Consider the Site
Faux wood blinds resist warping from heat and moisture and are a top choice for kitchens and bathrooms. Above windows with a window air conditioner, cellular shades are the best choice because they won't rattle noisily when the unit operates, the way blinds often do.
It's a Matter of Taste
Both faux wood blinds and cellular shades come in an array of colors. Both could be at home in contemporary or traditional decor. In addition to the practical questions, your choice comes down to what you think looks right.