Coins sent - visualise shows coins moved on - so I didn't send to another wallet of mine? Transaction ID:
6a1d9ab775f6b028a037deef37723fbf506947103f2c2f6e9c32149e0dffca34

I sent bitcoins in the above transaction.  I'm trying to determine if I sent to another wallet of mine, or to another person.

If I sent it to another wallet of mine, they would still be there, as I haven't spent them.

When I go to:
https://blockchain.info/tree/267511038

I see that the bitcoins have moved on to 
1Lw536Fvjg6KkCeAYetn7wopF3XEWbrY9y
and
32Vh3B83zoaRUsTahWTxpmcgnNXG727u7n

I'm concluding that I didn't send the coins to another wallet, but to another person, who has spent them.

amiright?
The transaction you posted has one output of 0.06193935 BTC to 1L6RYKMx4neDxVngWtsw59EteCxDfvADBk. The last time somebody spend an output from this address was today. 

Based on what you describe, it's probably not your address.