With all else being equal, the more frequent the compounding, the better the return on your savings. More frequent compounding has interest being credited to your principal balance more often, allowing the interest to start earning its own interest sooner. The miracle of compounding is all about interest earning interest. The "all else being equal" just means that we're comparing accounts with the same nominal yield and the same term, or time period, on the deposit.
The nominal yield is the stated yield on the deposit and is used to compute the interest earnings. It's not to be confused with the annual percentage yield, or APY, on the deposit, which takes into account how more frequent compounding increases the effective yield. By comparing APYs, you can find the financial institution offering the highest effective yield on the deposit. The Truth in Savings Act (Federal Reserve Regulation DD) requires that financial institutions provide the APY on deposits, so savers can make easy comparisons.
You earn a yield on your investments, but you pay a rate on your loans. That's how you differentiate between an APY and an annual percentage rate, or APR, on a loan. You can sort deposit yields by APY using Bankrate's Compare Rates feature.
APYs assume you're reinvesting the interest earnings. If you have those earnings transferred to your checking account, you won't see the interest compounded there -- at least not at the yield on the original deposit.