My yard turned into a pond after the last downpour and I'm stuck between two fixes

That heavy rain we had a few days ago left my whole backyard underwater for hours. A buddy of mine says installing a dry well is the way to go, but another friend thinks just adding more mulch and plants will soak it up naturally. I'm leaning towards the dry well cause it seems permanent, but the plant method is way cheaper and easier. Has anyone in Abq dealt with this kind of flooding before? I'm kinda stressed about picking the right option for our desert soil. Would love to hear what worked for you guys, lmao.