They can't sign two pitchers of similar age, price and contract term in the same year. If they want two, that is the advantage of using both acquisition methods. Either way, for me, the younger player who is controllable for more years should be well worth trading a few guys for. If that is not the case because the demands are unreasonable or the trade market is too competitive, then a free agent is a good alternative.
There have been no reports of them talking to Darvish, so let's assume they are talking to Darvish.
My guess is they only get one pitcher of any note, plus a bounce-back type guy. If the team is in the mix, they can acquire another pitcher at the deadline. Even if they aren't in the mix, they could do that, as some of these controllable guys won't get traded now, then will be available in July.