Is there much of a cost difference between the two?
Although the best answer would be 'check some printers', I'd say, yes, usually 4 spot colour printing is more expensive. At least for regular offset printing.
A typical printer will have their presses loaded with cyan, magenta, yellow and black ink, for this is the process that is the most commonly chosen. Changing the type of ink loaded into a press takes time and effort, and they're prone to charge that time to you, the customer.
Moreover, Pantone inks (the ubiquitous kind of spot inks) need to be mixed. I don't expect many printers to have all of the hundreds of PMS inks pre-mixed in stock. If you look at a Pantone colour book closely, you'll see recipes printed below any of the swatches—that's how the printer mixes the colour. Mixing takes time as well, and that time, you pay for.
It really depends on who is doing the printing.
Many mom and pop print houses don't have the capability to run process colors, so they will often farm out process work. They mark up that cost and pass it back to you. This can make process color jobs more expensive for those types of print houses. (Note: Some places like Kinkos do this as well)
However, if a print house as a web press or a process press, the actual ink used in the 4 color process is customarily less expensive than spot color inks. So their pricing for process work would be less expensive.
Ultimately, you simply have to get quotes/bid from various print providers to see where pricing falls.