Hello! They do not necessarily mean the same thing.
"deserving more" = talking about *quantity* (deserving a large amount of something than what you are getting now)
"deserving better" = talking about *quality* (deserving a better quality of something than what you have now)
However, depending on the context, they could mean more or less the same thing. For instance, we can interchangeably say "I deserve more than this" with "I deserve better than this!" in the context of talking about a relationship with someone that isn't working out. In this context, both mean feeling dissatisfaction in the situation
Hope this helps!