Which backlink checker you go for?
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There have been times when I couldn't find backlinks on Open Site Explorer that I could on SEO Majestic, so I like Majestic. I have not found much difference between ahrefs and Majestic in my experiences. I can't speak for linkresearchtools.com, however, because I've never used that one.
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MOZ and Majestic are the best two we have used. Ahrefs is similar, but personally I didnt like the visual layout.
We have also used Raven Tools backlink checker, which I did not see mentioned here yet. Just started using it, and like it very much. They also offer a free trial. Just because you have the money, doesnt mean you have to spend it.

Check it out here:
http://raventools.com/marketing-tools/link-manager/Hope this helps!
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Unless you have access to the website's Webmaster account, it's best to use a few and compare results.
Fore example, I've used Ahrefs and found links OSE didn't have, but I've also experienced it that other way around with OSE having links that Ahrefs didn't. Majestic is also good source, as mentioned.
I haven't found a completely accurate tool yet, I'm pretty sure it doesn't exist or the entire industry would know about it. Since you can't get it perfect, compare various databases and get as much information as possible.
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Strongly recommend Ahrefs and also - http://www.openlinkprofiler.org/ I know you said money isn't a problem but OLP is free and does a killer job, including lots of info that other checkers don't have.