When freediving, having the correct and EXACT weight is extremely important. I can tell the difference very easily when being off by just one pound when freediving.
For scuba, it sucks to have too little, but for an experienced diver, having 2-3-4-5 lbs extra ballast is not really an issue, since it can be offset by judicious use of the BC. I am not advocating for using too much lead when scuba diving, but the I am confident of the validity of my generalization.
So about the question... If you are using an aluminum tank and no steel backplate, you can probably try freediving and scuba diving with the same belt (as a first try). You will most likely be close, but it depends on a lot of variables primarily the depth of your freedive and not so much on your exposure protection. I would be surprised if the difference between your freedive and scuba belt is more than 4 lbs or so.
When you go to a steel tank and/or steel backplate, you will almost certainly need less lead on the (scuba) belt.
Generally, you want to weight yourself for freediving so that you are buoyant above 30 feet, neutral at 30 and become increasingly more negative - the deeper you go. Even with no wetsuit, the effects of chest compression on the freediver become significant below 50 or 60 feet. Also the deeper you expect to freedive, the LESS lead you will need.
Also, the scuba diver wears lead to counteract the effect of increasing buoyancy associated with the consumption of air in the tank. This is about 5 or 6 lbs for an aluminum tank and proportionally more for larger capacity tank(s).
So the difference is that the freediver has to deal with chest compression and the scuba diver has to deal with reduction in mass associated with air consumption.