关于几个英语的表达方式

这两种表达方式都对
基本上没有实质上的差别。

短语 a lot of work to do
可以理解为
a lot of work (for us/him/her ...) to do
的变体。
其他表达方式有
there is a lot of work ahead of us
much is left to do
much is left to be done
much is yet to be done
there is much to be completed
much work remains ahead
we ain't done yet; not by any stretch of imagination（口语）
等等，等等。
满意请及时采纳，谢
我是加拿大人，前英语老师。

1,There is a lot of work to do有大量要做的事 【强调事多】
2，There is a lot of work to be done有大量要做的事 【 to be done是 to do的被动形式，即工作是被人干的】3.4句一个道理。

to do表主动，要做某事
to be done表被动，某事被做

第二个只是单纯的有工作去做，而第一个有激励的意味吧，希望做得更好。