The main difference is that **tornar-se** has more focus on the transformation (but not necessarily with some progressive aspect), whereas **ficar** focuses on the final state. Remember that *tornar* can also be used in a similar way to "to turn" in sentences such as "ele tornou esta empresa numa das mais sucedidas no ramo".

As you may imagine, this still leaves quite a margin for overlap.

I assume you're referring to _become_ in the OED sense 5. Let's look at the definition and the examples:

> 5. To come to be (something or in some state).
>
> ✝ a. with _to_, _into_. _Obs._ [...]
>
> b. with _subst._ or _adj. complement_.
>
>   * [...] (too old for me to understand)
>   *  _c_ **1350** _Wilt. Palern._ 881 881 He cast al his colour and bicom
pale.
>   * **1398** TREVISA _Barth._ _De P. R._ v. lxii. (1495) 178 Goddis sone bycame man and dwellyd among us.
>   * **1483** CAXTON _Gold. Leg._ I35/4 So wyse a man is such a fole becomen.
>   * **1549** _Compl. Scot._ 2 The universal pepil ar be cum
distitute of Justice.
>   * **1611** BIBLE _Gen._ xix. 26 His wife looked backe .. she became a pillar of salt.
>   * **1625** BACON _Ess._ (Arb) 479 Their Boughs were becommen too great.
>   * **1717** LADY M. W. Montague _Lett._ II. xlvi. 30 The asmack, or Turkish veil, is become .. agreeable to me.
>   * **1774** CHESTERF. _Lett._ I. ii Unfortunately for her, she became in love with him.
>   * **1810** HENRY _Elem. Chem._ (1840) II. 699 When .. more
largely diluted with water, it becomes hot.
>   * **1848** MACAULAY _Hist. Eng._ 1. 4 When first they became known to the Tyrian mariners.
>   * **1876** GREEN _Short Hist._ vi. §4. 298 Florence .. became the home of an intellectual Revival. 

Note that these are historical citations and some of these sentences use the auxiliary "to be" instead of "to have".

I think the distinction between *something* and *state* that the dictionary does can help us. With _becoming **something**_, _torna-se_ will usually be the right word; and for _becoming **some state**, _ficar_.

So in Portuguese:

 * Ele perdeu toda a sua cor e ficou pálido. _("tornou-se pálido" would mean "tornou-se uma pessoa pálida", so a more permanent change)_
 * Pouco depois, Goddis tornou-se homem e viveu entre nós.
 * Um homem tão sábio tornou-se tão tolo.
 * O (?) universal ficou destituído de justiça.
 * A sua mulher olhou para trás .. tornou-se uma estátua de sal.
 * Os seus ramos (?) tinham-se tornado grandes demais. _("tinham ficado" is also possible, but I see here a gradual process where the boughs get bigger and bigger)_
 * O véu turco tornou-se .. aceitável/adequado para mim. _(the original has the present participle, which suggests it was a process. Actually you could never use "ficar" here. At some point something is acceptable or it isn't -- so you would use "ser"; it can become acceptable through time though, and then you would use "tornar-se")_.
 * Infelizmente para ela, ficou apaixonada por ele.
 * Quando mais diluído em água, fica quente. _(or "torna-se", if we want to focus on the process)_
 * Quando os marinheiros de Tiro ficaram pela primeira vez familiarizados com eles.
 * Florença ... tornou-se o lar de uma renascença intelectual.