I noticed this when my children were babies. Despite the totally dry pregnancy followed by two years of breastfeeding each (over 5 years in total completely alcohol free) the sleepless nights always felt like a massive hangovers. Only they are not. Once you get to sleep, you fully recover. It takes much more than a good night of sleep with alcohol.
It took me about 18 months to start sleeping better after I quit. Now I feel rested and renewed every morning. Sleepless nights always give me a nasty edge, but never the anxiety, shame and sadness of alcohol (or the 3 am horrors)