I think Litecoin is firstly more estabalished with new features being introduced along the way like the Pay feature in addition to better acceptability & recognition vis-a-vis NEO (as of now) and should touch $1000 in 2018 before NEO.
Whats your view...
Both of them have the potential to reach that level easily as soon as bull run hits the market but there is still time for that period.NEO now is getting hype and popularity due to support from china.So NEO can touch $1000 level first as litecoin will get price boost when prices of btc will rise.But lets see who wins the race.