As far as I know, the methods perform similar for most applications and differences mainly affect edge cases such as supplementary alignments. Another option would be samblaster which I use in my ATAC-seq pipeline. In the end it probably does not matter. The advantage of samblaster/samtools over Picard is that it uses way less memory and can be used in Unix pipes. In ATAC-seq it is not uncommon to have some duplication, probably due to mitochondrial contamination. I would not worry too much about that and rather see if the downstream analysis indicates good quality (number of callable peaks, Fraction of Reads Per peak, good signal-to-noise ration when inspecting reads in a genome browser = distinct peaks without much noise).

Unless something has changed dramatically, you should use Picard and not samtools to mark duplicates in an aligned file. Even Heng Li (the author of samtools) said that he does not recommend using samtools markdup. The topic was discussed quite a lot, for example, here: http://seqanswers.com/forums/showthread.php?t=6854

If you need to remove the duplicates, make sure you set the appropriate flag in Picard MarkDuplicates.