两者词意、用法均不同；

eat up ：

1.吃完;吞噬

Eat up the dinner while it is still warm.

趁饭还热,快把它吃完.

2.消耗;用完

The work ate up all his time.

那工作占用了他所有的时间.

eat out

1.上馆子吃饭

They usually eat out on Sundays.

星期天他们通常上馆子吃饭.

2.锈坏;使腐烂

Rust had eaten out the gun barrel.

枪筒已被锈蚀.