How to choose which reactants to have in excess?
Sometimes the excess is the cheap/unlimited reagent you use to get a high yield on your expensive/limited reagent, and sometimes you use the one that you don't mind/can easily extract from the products.

In this case, if you wanted to collect and record the lead(II) sulphate as a precipitate, using an excess of the lead(II) nitrate would be a waste.  If your intention was to produce a large quantity of sodium nitrate solution, and you don't mind having a load of the lead nitrate contaminating it, then you could use an excess of the lead nitrate.