Not, as far as I know.
"Se me hace mejor" expresses a preference, making a comparison; like saying "I find this better than that".
- Se me hace mejor cantar que bailar. -> I prefer singing to dancing. I find singing is better.
- ¿No se te hace mejor pedir un vino tinto que uno blanco para la carne? -> I think we shouldn't order a white wine for eating meat, and I'm asking you if you wouldn't rather order red.
- En casa no teníamos videojuegos porque a mis padres se les hacía mejor darnos juguetes convencionales. -> Our parents preferred giving us any other kind of toy rather than videogames.
If you say "se me hace mejor hablar inglés que español", you mean that, comparing both languages, you like speaking English better than Spanish.
"Se me da mejor" means that you find something easier to do than something else.
- Se me da mejor hablar inglés que español. -> I can speak Spanish, but it's easier for me to speak English.
- Soy panadero porque siempre se me dio mejor la cocina que cualquier otra cosa. -> I could have chosen any occupation, but cooking meant less effort or less hassle than anything else for me.
- Se me da mejor cantar que bailar. -> I can sing, but my dancing skills could improve.
