How do I know my git repository is same as my Mercurial repository?

You cannot compare SHA1 hashes between Git and Mercurial (they would be different anyway)

But you can at least script and compare:

• the list of revision in Hg (with their comment)
• git log (which includes comment)

And see if the list has the same number of elements and if the comments matches

For each commit, you can:

• list the files in a given Hg revision (hg status --change <rev>)
• list the files a commit

And make sure each one:

• has the same number of files.
• has the same content, by comparing them with a diff tool (kdiff3 or, as suggested below, WinMerge if you are on Windows)

Using a diff tool alone is not enough: you need to do it revision by revision.

If you have a copy of the original HG and new Git repos locally, you can use a program like WinMerge to diff both folder trees.

Excluding the "internal" files like .hg you should find an identical set of files at the heads of both.

Personally I like this approach because it is independent of the source control systems themselves. If you don't fully trust the Git conversion in the first place, I think its sensible to check the "facts on the ground" directly without going through any extra intermediate steps.