I'm considering changing my gear ratio on my SS. I am currently running 42X18 and I am thinking of maybe switching to get closer to 70 GI.

All things equal, does it make more sense to change out the freewheel or the chainring and why? I've priced out both, and it is pretty close to a wash, so does changing one over the other offer any advantages?

While you might be able to get away with a small change in cog size, changing the chainring might require you to have a longer chain.

Depends on what you want to go to.

I'd get a bigger ring if I were you. I'm pretty sure larger chainrings and cogs last longer than small ones. Don't remember where I read that, but it makes sense; more teeth = less wear on each individual tooth.

A freewheel should be cheaper than a similar quality chainring. So unless you are getting a top of the line freewheel, or a bottom barrel chainring the freewheel would be the cheaper option/

Actually, they are probably closer than you think. A Shimano freewheel will run between $20 to $30 depending on where you purchase. I believe an eighthinch chaingring is about $25. Alternately, you could get an Eno freewheel or a Sugino Messenger Chainring, which are both in the same ballpark, but substantially more than the other two.

Eightinch chainrings are bottom of the barrel

I've had a couple that were pretty damn good. In that price range, there are a lot worse.

I've been riding a used one for a while now and I get pretty even chain tension with it

And eightinch chainring is a competent chainring. But it is not a high quality ring. A good $20 shimano freewheel is not its "equivilent" that would be something along the line of an acs claw which is $10

So, if I am speding $20 to $30 on a freewheel, what would be equivilent in terms of chainrings? I had heard good things about the eightinch, which is why I was considering them.

I have an Eighthinch crankset on one of my rides and while it may be cheap $50, I've had no problems with it and it looks nice.

To answer your question, I would just buy a shimano freewheel in a smaller size so you don't need to buy a new chain as well. Then down the road when you are itching to get a new crankset you won't have to worry about upgrading your freewheel.