The first sentence uses a non-essential clause, the second an essential clause. Both are grammatically correct but the emphasis does change slightly.

I possibly prefer your revision but you can’t state which is wrong or right as I’m stating an opinion, so the importance of the sub clause to the first part of the sentence is really up to me.

Anyway, it really isn’t worth worrying about…

‘[P]eople are confused about which and that… This isn’t surprising, as there has been a shift in usage over the past century or so and older guides give different advice from newer ones… If you wish to write naturally, don’t fuss too much about the usage of that versus which. Obsessive correction (sarcastically called a which hunt) is best avoided’ (http://www.worldwidewords.org/articles/which.htm)

Jon, ‘they’ has always been used for the 3rd person singular when the sex of the person referred to is unknown – Though it may be used more in these pc times, I’m pretty sure I remember my Latin teacher suggesting it came from that language, so hardly a modern phenomena!

This is a really great site, which provides clear explanations of some complex grammar issues for free. Jon, you should really check your facts before posting confrontational comments!

You’ve just made too many mistakes to correct them all in one sitting, I suppose.