Well 3/4" mdf is 1/8" thicker than 5/8" mdf (DUHH). i dont think there will be that much of a difference, but 5/8" is the cheapy stuff, and will cause the box to flex easier (because its thiner). Therefor losing some some edge on the 3/4". Conclusion: 3/4"
There will be an audible difference. The 5/8" MDF will resonate at a different frequency than the 3/4" MDF. The 5/8" MDF will sound boomy or boxy. The 3/4" MDF will have better controll.
Test it for yourself;
Go knock on a solid wood desk and listen to the sound. It will be a high pitched sound. Now knock on your hollow 3/16" thick door-skin and listen to the sound. This one would sound low pitched with an echo.
Why?
Because it vibrates...
When building a speaker enclosure, you want to hear the speaker's resonance, not the box.
Prefferebly use 1" MDF. Believe me !!! You will never go back to lower thicknesses.