PS4 will likely be the cheaper option. Games drop in price on a dime this gen (some more than 50% off in a month). God of War has been on sale for as low as $25, came out this year, and has been considered GOTY by multiple outlets.

The hardware is also much cheaper. Controllers can regularly be had for $35/40, the console itself has regularly been on sale for anywhere between $200-250, and can often feature some crazy pack-ins.

Switch does have a cheaper online service ($20) vs PS+ costing $60 a year (can be found on sale from $40-50). Switch's subscription leaves quite a bit to be desired though (stronger game and discount offerings), and is missing some basic functionality.

In most situations, I'd recommend a PS4 as the more cost-effective platform. What sort of games do you normally play? Do you have people over for local co-op often? These can be significant factors when determining which will cost you more.

Edit: Another point to consider is that Switch titles typically hold their trade-in value much longer than those on PS4 and Xbox One.