In the UK we have significant tax-breaks for investors.

Up to £150k (~$250k) investors can get up to 86.5% of their investment back from their tax bill under the Seed Enterprise Investment Scheme (http://www.seis.co.uk/) with no capital gains on profits. That means the total "at-risk" capital may only be £20.25k

The average seed stage valuation looking at crowdcube, seedrs etc looks around £600k ($1m). But given 86.5% capital protection provided by the government, a £150k investment (enough for a prototype for an app say), which would be 20% of the company post-money, would actually only have £20.25k of "risk" capital. That means the company's real "at-risk" post-money valuation would be £101.25k ($165k), a twentieth of the Angelist number and a thirtieth of the Pitchbook number. Even lower than most accelerators.

Above £150k investment there is the Enterprise Investment Scheme, which offers up to 61.5% capital protection from the government up to £5m in investment.

Are UK investors just considerably more stingy or am I missing something? Do American investors get tax breaks above reductions in capital gains if things go wrong?

The 86.5% and 61.5% numbers are if the company fails completely. Otherwise if the company does well, you still get 64% and 30% of your money back as an investor for SEIS and EIS investments respectively.