You can use either as the P6BAT-Me supports both - it'll have these slots - click here for a pic.
Doing a search (at click here), I found a list of compatible CPUs for the P6BAT-Me with PCB v2.0 & BIOS v5.5: click here (scroll down if necessary).
Also see - Pentium III CPU Support List click here
I couldn't find info regarding the same with P6BAT-Me PCB v1.1 - only a whole load of download links click here.
Download the P6BAT-Me manual by clicking on the appropriate link at click here.
As you're overclocking, this may be of interest - "The benefits that the new generation of Coppermine Pentium III's offer is on-die L2 cache. This cache runs at the same speed as the CPU does, and is of a higher quality than off-die cache. Because on-die cache can run at the same speed as the rest of the processor, performance is increased - even when the on-die L2 cache is smaller than that of the older off-die cache. Because of this, you are able to overclock these processors with a higher success rate than the older generation of Pentium III's." - from click here. For another P3 overclock guide click here.
Good luck with it all. G