I also have the same issue (as will everyone selling to the 700 million who live in the EU). As they say, lifes only certainties are death and taxes; sadly, one simply can't decide not to pay tax
Fixing presstashop is probably a long way off - so as an interim, please can we have a splash label on the site to say all prices inc vat at xyz% to inform customers.
The basket should always quote the ex-vat price and then always add the appropriate % VAT to the ex-tax price at checkout. With a B2B shop, shopper gets to choose which style of pricing they'd like to see. This is how all mid tier shopping cart software works in the UK - eg www.toolstation.com
The correct logic for prestaShop to use (and it doesn't) would be to display either inc VAT or ex VAT pricing depending on the selection made in prestashop, and then apply tax (always apply tax) at the checkout. The final price should not change according to option "to display" or to "not display" taxes because VAT is always payable always. technically, VAT is still charged on exports as well, just its at 0%. In prestashop, (if tax was correctly coded) this could occur via tax zones.
At present if the shop quotes an ex-tax price the final price is also tax free. This is wrong.
The use of the ex-Tax option will always produce the wrong price in the EU because as already said, tax always has to be charged. A business buyer still has to pay VAT, they just claim it back from the taxman. The exception to the rule is sales between eec countries for businesses (not retail), when vat is charged at 0%, but it must still be itemised on the invoice as a 0% item.- there are prestashop modues that do this.
Bellini13's point about what rate to charge is valid - how is Prestashop supposed to know where a customer is until after they signup. There is no foolproof approach here, so either the inc-VAT option isn't available until someone signs up, or a notice advising that a default tax rate of xyz% (probably the rate of same-country shoppers) is applied to annonymous shoppers. By using the correct logic of applying VAT to the basket means that there is an oportunity to amend the price during the checkout process as soon as a "country of residence" is provided.