I'd always go wired since i'm old school...
Googling "max cat6 length" would return results indicating the longest run of a CAT6 cable to be 100m or 328ft for optimum performace for 10/100/1000BASE-T. Note this maximum allowed length consists of 90m or 295ft of solid "horizontal" cabling between the patch panel and the wall jack, plus 5m or 16ft of stranded patch cable between each jack and the attached device.
Further, googling "max length for burried cat6 cable" would provide even more info on the type of cable to use and issues you may have. For example, it's best to run cable inside 40m pcv pipe while using "gell filled solid core" cable otherwise "direct burial" cable should be used (some use direct burrial cable inside piping - to be sure to be sure). The piping should have wide arc bends if any as it reduces cable stress when pulling wire. You may also read that it's not a good idea to run power and ethernet in the same piping as power and ethernet cables should be separated by 30cm or 12" (from memory?) when running these cables run parallel to each other (this then dictates a wide trench and twice the piping). There are also issues with earthing that can impact noise levels and thus data throughput which must be handled correctly (as should lightning protection on external cable runs be they above or below ground).
So in your case, if all issues are catered for, you wont get optimum GBE performance with a 400ft (+ 16ft at each end?) cable run but it could be close and you should get something >>100Mbps but <1000Mbps
Otherwise consider optic fibre with
GBE to OF converters at each end as this removes many of the earthing and lightning issues you need to consider while providing longer cable runs in the process (550m to 70km)
But the best advice when digging any trench is to drop in some more piping and extra cable/draw string for future use "just in case"... After all, nobody want to dig up a trench a second time
Do note that while wireless avoids many of the above issues and may be simpler and cheaper, airwaves will only get more congested as time goes by so what works today may not work as well when your neighbors install their wireless systems - your wired networks, if designe well, will always work
