A few interesting things about this.

1) Amex the same price as other cards. Amex has low penetration among small retailers in the UK because they traditionally cost a lot more to accept.

2) Square are very up-front with costs. All the major banks hide their costs - requiring you to call their sales weasels to get a quote.

3) The card reader cost is the same as PayPal - but Squares costs are fixed @ 1.75%. Paypal's are 1.5%-2.75%. The same applies with iZettle - there's a variable cost which is quite opaque for small businesses.

Essentially, if you don't want to jump through hoops and worry about getting screwed over by small print, it looks like Square is compelling.