By my point of view (as a Brazilian), "tomar" is closer to stealing. Although both can be used in this context, "ela tomou minha capa" seems (to me) like she stole my cape or, at least, she took it without permission, or against my will. In Brazil, "tomar" can also be used as "beber" (drink). Both are correct, but one is slightly "stronger" than the other.
"tomar" is a more "strong" verb, mean almost to steal something; to take without permission; "pegar" is more close to "grab"; "you grab something" = "você pega algo"
They are not that far in the meaning though, you can use both without much problem with the understanding! ;)