"better profit" but only in the eyes of accountants, for a while.
The money you've paid less tax on is still offshore. If you want to bring it back to your country then you have to pay tax on it (minus what you've paid already overseas) so it's not just a simple scheme to minimise tax. If you need the money to maintain cash flow then you've got no real choice but to pay full whack on it to get it back into the US.
What many US companies are doing is hoarding huge piles of it overseas in the hope that the US will have another tax amnesty (like 2004) and they can bring it back in to the US without paying as much tax as they would have had they just paid it in the US in the first place.
Here's a simplified example based roughly on real figures.
Take a US company that makes a $1bn profit in a year. They would have to pay 35% tax on that if they kept it in the US.
Using a Double Irish Agreement and paying a $1bn fee to those foreign entities in Ireland/Cayman Islands they make $0 profit in the US and pay $0 corporation tax. In Ireland they pay 12.5% tax on that money, so Ireland get $125m.
Meanwhile the cash sits overseas and the US company can't use it. If they wanted to bring it back to the UK they'd need to pay a $225m tax bill (35% tax on $1bn minus what is paid overseas); it's unsurprisingly more complicated than that but we'll leave it simple. It's also earning interest overseas but we'll ignore that for this example.
What they can do is bung this $225m on the balance sheet as a future tax liability, since if the worst happens and they run in to cash flow problems they'd have to bring all of the original money back into the US and pay remaining tax on it. Ironically, this means they can offset even more profits against this liability.
Anyway, they wait until the US has a tax amnesty for bringing back money from overseas (last one in 2004) and then pay a fraction of the tax they would have originally. The current campaign is for an amnesty rate of just 5.25%
How much is this used, and on what scale?
If you believe the numbers in this article: http://news.yahoo.com/apples-phantom-taxes-hide-billions-pro... then Apple has $74bn in cash accounts overseas.