The danger with charity in place of tax is that it is directed at what people care about, not at what society needs so that unpopular causes (helping drug users and such like) is likely to be ignored in favour of pet charities.

I think the whole situation is further complicated by religious giving - Romney being a good example of it. Firstly, in the US, they are opaque organisations which means it is hard to assess what % of donations actually is spent on charity and what is spent "internally". Which leads in to secondly, what actually counts as charitable as Mormons might see $5 million spent on baptising the deceased of other religions as extremely charitable while for non-Mormons that might be a questionable use of the money. Thirdly, what value does allowing people to offset chartible donations against tax offer, in particular when it is giving to a church - if someone has to give a set % as a tithe, then are they going to refuse to if they can't offset it against tax.
I'm also not sure that letting people give to a church instead of paying tax counts as giving to Caesar what is his (or however that was phrased)