As they are similar in chemical composition I would expect that both would persist for a similar amount of time. However perhaps the circular nature of the mtDNA may protect it from environmental nucleases to a higher degree. Certainly the early studies looking at human migration out of Africa focussed on mtDNA sequencing, but this may have been due to the fact that a complete mtDNA genome is only ~ 16kb and therefore full sequences could be more easily recovered and compared relative to the much larger genomic DNA sequence. Apologies for not giving a precise answer but I'd bet more on mtDNA surviving purely due to abundance and circular structure! I'd look into the work of Svante Pääbo and colleagues as they have a long track record in recovery and analysis of ancient DNA samples.

just to add to Martin's comment (hi Martin :)) you will have more copies of mtDNA per cell than nuclear DNA hence you will have a better chance of recovering useful information if not complete sequence.

Hi Treena - I agree with the above comments.