I'm still using a 6870 to play 1080p on my TV and usually play on high or custom settings. Things still look great and with the proper tweaking it can run really well.
A 780 will last a long long time in computer terms, especially since you will probably replace the machine in the 2-4 year range anyway.
Seriously, without knowing what's coming up from upcoming games and how tech will change, there's no way of telling how long a 780 or 880 will play on highest/high.
There's no way to answer that unless you know someone who can see into the future. The 880 hasn't even been released and all the available specs are just speculation.
I'm still using a 6870 to play 1080p on my TV and usually play on high or custom settings. Things still look great and with the proper tweaking it can run really well.
A 780 will last a long long time in computer terms, especially since you will probably replace the machine in the 2-4 year range anyway.