The general position, stated factually and not as advice, is that a spread bet is legally a bet, so gains are not usually subject to capital gains tax and no stamp duty arises on the underlying. The corollary is that losses cannot usually be set against gains elsewhere, which is a real cost for anyone who expects losing years.
A cfd is treated differently: no stamp duty, because nothing is bought, but gains are generally within the capital gains regime and losses can generally be offset against other chargeable gains.
Two caveats are important. Treatment depends on an individual's own circumstances, including whether the activity is judged to amount to a trade, and tax rules change. Anyone relying on the difference should confirm their position with a qualified adviser or the tax authority rather than a broker's marketing page.
Example: two traders each make GBP 20,000 of profit. The spread better's position may fall outside CGT entirely; the CFD trader's gain is generally chargeable, subject to the annual exemption and their own rate.
Related: spread-betting, cfd, fca, cfd-vs-spot-fx