Taking a deduction merely reduces taxable income. Taking the credit reduces tax. Therefore, in MOST (but not all situations) taking a credit is better.
For example, if you have $1000 income and owe $250 tax, and paid $400 tax in the UK, then taking a deduction would reduce income to $600 (and thus tax to $150), whilst taking the credit would reduce tax to nil, and you'd have $150 to carry forward against next year's tax, if necessary.
I can only think of two advantages to taking the deduction as opposed to the credit.
1) It is simpler, especially if you itemise anyway.
2) The Credit is limited to the percentage of foreign income, so you can't use it against US income. The deduction can be used against US income. So if the US income makes up the bulk of the total income, and the UK tax on UK income is high then a deduction may be worthwhile.
Nevertheless, in almost every case, the credit is going to be the best choice.