"She is as beautiful as her mother."
Translation:Lei è bella quanto sua madre.
Did you get "Lei è così bella come sua madre" as an answer? In that case, the literal translation is "she is So beautiful LIKE her mother." Caps just to illustrate così and come. XD anyway, this sentence is relatively similar to "she is as beautiful as her mother," so it's accepted.
"Tanto ... quanto" implies quantity, so you're putting their beauty on a scale and comparing; "così ... come" implies quality, so you're saying that their beauty is similar, or that they're both beautiful. The nuance is hardly meaningful in contexts such as this. By the way, the first elements of the comparisons, "tanto" and "così", can be omitted, and usually are, I only put them in for clarity.
You don't use "come" or the correlative "cosi... come" when comparing nouns. Only use them with adjectives. :)
You can read more here: http://tutorino.ca/grammatica/2007/2/19/comparing-things-in-italian-equality-as-much-as.html