The difference between the two is 0.000001, and the difference in quality of approximation is roughly 0.0000003. So I don't think it matters as a practical preference. Aesthetically, the string of digits of Pi has a cultural significance of its own, quite apart from its numerical value, so I think it's preferable to memorize a number that's actually a prefix of that string.

Also, only if you truncate can you truly say that you've memorized "the first six digits of Pi after the decimal" as opposed to "An approximation of Pi to plus or minus 0.0000005 tolerance".