Albacore or Yellow Fin
The Environmental Defense Fund has made a few recommendations based on EPA guidance:


  Canned white, or albacore (0.32 parts per million of mercury). Children under six can eat up to one 3-ounce portion a month; children from 6–12, two 4.5-ounce portions a month. Adults, including pregnant women, can safely eat it up to three times a month (women, 6-ounce portions; men, 8-ounce portions).
  
  Canned light — the safer choice (0.12 parts per million of mercury). Children under six can eat up to three 3-ounce portions per month. Older children and adults can safely eat it once a week. But look out for "gourmet" or "tonno" labels. They are made with bigger yellowfin tuna and can contain mercury levels comparable to canned white.
  
  A better alternative is canned salmon (mostly sockeye or pink from Alaska), which is low in contaminants and high in heart-healthy omega-3s. It's also sustainably caught in Alaska and similarly priced, making it a great choice all around.


They may say "safer choice" but what it comes down to is that regardless of which type of tuna you eat, you're going to be getting a pretty high amount of mercury if you eat it frequently. Mercury accumulates in animals higher up in the food chain. I hate that I'm screenshotting an svg in order to post it but below is a helpful little diagram:


- via Wikipedia

I included the part regarding salmon from the EDF source because salmon is just a better choice to make environmentally and for your health. I know your question was albacore versus yellow fin, but the difference there is negligible. The light vs white is a matter of which cut of the fish you get and that does matter, but you're still getting a fair amount of mercury. Eat smaller fish, like salmon, herring, sardines, kippers, etc. if you are truly worried about mercury.