This depends on the console you are using and the upgrades you have. Here is a simple chart to help you out.

It's all about the watts. Let's use the GBA as a starting point. Your standard 2x AAs of 1200mA batteries have 2.88 watts of power. The best AAs on the market 2x AA Eneloop Pros have 6 watts. The CleanJuice has 6.29 watts. More power = longer life.

Game Boy Advance

The GBA stock uses 0.28 watts of power. So for AA batteries that is 2.88 / 0.28 = 12 hours. Now batteries are not perfect, so normally you take off 15% so 12 * 0.85 gives about 10.2 hours of gameplay. That's the basic math used, and either way, accurate or not, the comparison between power sources is perfectly accurate as it is based on actual wattage.

DeviceAAsEneloop ProCleanJuice
Stock GBA (0.28W)10.2 hours18.2 hours19.1 hours
IPS GBA + CleanAmp (0.495W)4.9 hours10.3 hours10.8 hours
IPS GBA + CleanAmp + EZFlash (0.9W)2.7 hours5.6 hours5.9 hours

Note: We do NOT recommend the EZFlash range of products. They are very low quality internals, and insanely power hungry, using more power alone than the entire console + IPS + CleanAmp on full volume. Save your batteries and your nostalgia and buy original games! (or at least get an Everdrive :P)

Game Boy DMG (Original)

The CleanJuice for the Game Boy original comes in 2 sizes. Regular and XL. Using the same formula above here is the chart for the Game Boy Original.

4x AAs at 1200mA have 5.76 watts. 4x Eneloop Pros at 2500mA have 12 watts. And the CleanJuice regular has 9.25 watt with the XL having 11.1 watts. 

Eneloop ProCleanJuiceCleanJuice XL
Stock GB (0.32W)15.3 hours31.8 hours24.6 hours29.5 hours
GB + IPS + CleanAmp (0.7W)6.9 hours14.5 hours11.2 hours13.5 hours
GB + IPS + CleanAmp + EZFlash (1.2W)4 hours8.5 hours6.6 hours7.9 hours

Source: RetroSix Knowledge Base