Their respective risk is directly related to how you handle and use each of them. Certainly you can minimize lead exposure due to inhalation by not smoking during or directly after handloading (I imagine there are some idiots that may actually smoke during the loading process!), shooting, cleaning, and by washing your hands well with a good phosphate based detergent (that removes the lead by complexation) or one with a citrus base and mild abrasive action, like GoJo, after handloading, cleaning or shooting.

It requires somewhat less effort on your part to handle jacketed bullets for handloading since there is less direct contact with lead. However, you will notice that some bullets, e.g. 45ACP 230 FMJ from certain manufacturers, may actually have lead exposed at the base. While this minimizes overall exposure, there is still lead contact. Another potential source of contamination is brass cleaning, because the brass will have been exposed to lead from firing due to the lead styphnate priming material. It will be there whether you use jacketed or lead bullets, and is an area where you need to practice good handling to minimize both inhalation of dust and contamination of the area where you do it.

During firing, indoor vs. an outdoor range is a significant consideration, over only some of which you will have any control. Indoor range management of dust and powder residue is a factor as is their air handling/filtration system. A significant portion of the contamination residue just ahead of firing positions comes from primer combustion (lead styphnate) and powder residue. Whether lead bullets or jacketed ones are being used is possibly significant, but it is overall range use that counts rather than your specific contribution. Some of the "clean" ammo is using lead free primers and "totally enclosed" bullets, but it is still less common that standard except where some high usage training facilities have required it. On outdoor ranges, you would prefer to have the wind blowing away from you, but more significant exposure would occur if after shooting, especially after cleaning (remember the primer residue), if you did not wash your hands and possibly your face too before eating or smoking. Digging through the range backstop for bullets or picking up spent brass also increases risk of contamination.

Are lead bullets more prone to increasing your lead exposure? Certainly from a potential contact and handling perspective they could increase your exposure risk if you use poor handling techniques. But it is not as much a factor as how you practice range and loading hygiene methods.

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