If both handsets are rooted, I suppose you could backup the apps with Titanium on one and restore them on the other with TB. I don't think it would cause any issues if both were linked to the same gmail account.
If you head to the market website, log in with the gmail account associated with the phone, hit My Library, then apps, you'll be presented with a list of all the apps you've ever installed. You can remotely install them from there too.
I can confirm the market will remember the apps downloaded from your gmail account. I recently did a fresh ROM install and all apps were trying to re-download after signing into my Google account.
The better option if you're rooted as mentioned above is to using titanium as it will also copy over settings and saved data
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