A good start would be what is proposed in the press release: Harmonized VAT rates and rules for digital goods.
The problem is that unifying VAT and classifications basically regulating half a tax system without regulating the other half. You can tax income and you can tax consumption and there's pros and cons to both. If we're forced to lower our VAT, the other taxes would probably increase to compensate or the other way around. In addition many of the VAT brackets are made for a specific purpose because the goods are either particularly good or bad for society, like taxing books less (knowledge is good) and tobacco more (very bad for public health).
For example, around here we have about half VAT on food. If we can't keep that exception, prices would rise 10%+ on the spot. So would our taxes, in practice we'd probably funnel that money into agricultural subsidies instead which would make our food cheaper, thus creating an even more heavily protected, subsidized agriculture. And the things we want to punish, just add other taxes instead of VAT, unless the EU wants to regulate all consumption tax. That would be a tough sell, I think.
What products and services end up in what VAT bracket is sometimes controversial, for example here in Norway at the moment there's 0% VAT on buying a physical newspaper and 25% VAT on a digital newspaper, because it doesn't meet the criteria for an exemption. Also eating at a restaurant and takeaway ended up in different brackets, so if you take your burger outside and eat it on the sidewalk it's cheaper than sitting down at McDonald's. We have an exception for culture, they were probably thinking more like theater, opera, concerts but exotic dancers won at court as an "artistic performance".
Not saying it can't happen, but if it does it's a big step on the way towards a "United States of Europe".