Hi Kymie and welcome aboard. We have used both WDW's and DLP's on many occassions. They are very different fom one another.
WDW's is full of silly fun and is a great place for fun, especially for kids (our youngest had her first haircut done there, and our 4 year old had his hair cut, then green gel including mickey mouse in the back of his head.
DLP's is aimed at pampering men. It is about having traditional hair cuts and straight razor shaves in an old fashioned way. I love having a shave at DLP, so relaxing, and I become a part of the show. Not for kids or women.
I love them both for different reasons. Another big difference is you can just show up and queue at WDW, at DLP you must have an appointment.