Собирательные числительные (вдвое, втрое, etc.) are a bit more colloquial but totally acceptable in everyday speech and in literature.
Both forms are correct and common.
The main difference is that "в X раз" is not limited in the number of times, while собирательные числительные go from 2 to 10. You can say "Акции компании за несколько лет выросли в цене в 12 раз", But you cannot say "в двенадцатеро". In practice only "вдвое и втрое" is widely used, starting with "вчетверо" and up it's more likely to hear and read "в X раз".
Much like in English you can say twice and thrice (and the latter is rarely used) and that's it. After that you just use 'X times", though you can say in some instances that something has doubled, tripled or quadrupled. Again, can only go to four. You of course can go with Xfold as high as you want, but it's rarely used outside of articles and books and it's yet a different form. So realistically after 3 in English "X times" is used.
Also the bears that are twice as large as human are extremely tiny ones. The truly huge ones are 6-8 times bigger. Kodiak and Kamchatka brown bears reach over 650 kilos and 3 meters in height :)