Not sure if you're also asking for a strategy or just the "best" trading time. I can/have traded them all, and it really depends how you define best, especially given there are no guarantees on consistent performance.
But overall, 6E moves the smallest range during the Asia session, often retracing what NY did, or, moving about 30 pips in one direction and then returning to where it started. London range can be all over the place but you're most often looking at 80-120 pips of late; sometimes the moves are completed prior to any 9:30am London news but just as often they are not. You have your fakeouts, you have constant buyer/seller and level defending going on. Pre New York can see a shakeout, or not. London declines had for a time been reversed thus bought-up by NY at some point (after a shakeout). The NY session tends to be closely correlated to the ES and equities, and will often add that much more to the average daily range.
I realize that doesn't help much. I suppose it depends on how well one can apply a strategy - 10 pip per day can be had in either and much more. Strategies abound - perhaps a strategy using POCs or today's opening and closing levels plus previous day's closing and opening levels can be a place to start.
personally I think one's trading hours should be based on one's lifestyle and family
commitments rather than thinking there's a particular session or hours in a session
or particular hours in a particular session that's going to guarantee a large price move
if you don't have one, download a MetaTrader 4 demo program and install the zipped
indicators in: C:\Program Files\Broker\experts\indicators
i-P Time - displays vertical lines: green line is the start of the available time I have to
trade and the red line bedtime - I'm on the West Coast
NB: you have to use the MT4 Moscow time when setting the lines, also re-configure
chart below to ESTime
MT4: 00 01 02 03 04 05 06 07 08 09 pm | am 10 11 12 13 14 15 16 17 18 19 20 21 22 23
PST: 3 4 5 6 7 8 9 10 11 12 pm | am 1 2 3 4 5 6 7 8 9 10 11 12 1 2 - - - - needs re-spacing
i-SessionLn - displays rectangles of the Asian, Euro, US sessions, either background
filled or just a dotted outline - white on the chart for the Euro session
the gap between the Pink US and Goldenrod Asian sessions is one hour the closure
of the Globex markets
Grid_v2 - horizontal lines display any pip amount between them - 20 on the attached 60min chart
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Personally I love the London open for EUR/USD or 6E. Only for the first hour and a bit though.
NYC open is nice too, but I find I perform better during London's open (historically speaking, I can't argue with the numbers.) Plus I'm so focused on equities during the NYC session, especially during equities open and the first two hours of equities trading, so I can't give spot fx the attention it deserves during that time.
Sadly though, since I'm in the EST timezone, I hardly get a chance to trade the London open as I can't operate on just a few hours of sleep during the week (need to be fresh and rested on weekdays.) A friend of mine does it, sleeps early, wakes up for london, trades for two hours, then sleeps some more before work in the morning, but such a schedule would make me a zombie. lol