Well the only quantitative measure of the effects of any UI interaction is the change (positive or negative) in user behaviour.
A/B tests are one of the best ways to get clear reporting of how the changes are affecting user behaviour. The matrixes can be widely different.
The most common one is conversion rates in case of the call to action methodologies. If the changes you suggested/implemented are creating higher conversions (clicks, purchases, subscriptions, downloads or anything that applies to your solution), then it's safe to say that your solution is more "effective". It can also be measured simply by comparing numbers from testing both solutions in a real and/or simulated environment.
This can be applied on pretty much any UI changes. A/B testing is an industry on its own now. The measurement of impact can vary from time spent on page to purchases made by users - depending on the results you can report and discover exact impact of changes you've made.