Imam al-Shafi'i (may Allah have mercy on him) said: "It will be said (to him): 'You are both equal in the claim and in the proof (testimony), and the one in whose possession it (the item) is has, by virtue of its being in his possession, a ground that is stronger than your ground; so it will be his on account of the greater strength of his ground. And there is (also) a Sunnah on this matter in line with what we have said.'"
Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) said that two people made a claim over an animal, and both had witnesses that it was his mount; so the Messenger of Allah (peace and blessings be upon him) gave judgement in favour of the one in whose possession it was.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الدعوى والبينات / 21223