To return the sheet index containing the largest value try:

=MATCH(1,FREQUENCY(MAX('1st:End'!D3),'1st:End'!D3) ,0)

" wrote:

I have a productivity spreadsheet, where I track the productivity
numbers for a number of individuals. Each worksheet ("tab" if you
prefer) is a different persons name.

Each tab has columns for: A: week#, B: time, items, C: errors, D:
items per hour, E: accuracy.

I know I can find the max value across the sheets by using:
=MAX('1st:End'!D3), but that doesn't tell me which person achieved
that number.

I'd be happy with it either returning the tab name, or the contents of
cell A1.