I noticed some old wagon rims at a local antique store. I have not looked at them up close but was wondering how to detect wrought iron over mild modern iron. Is wrought iron good or better as a forge material.

Wrought iron will usually display a grain like wood does if it has been corroded sufficiently.  Other than that, you'll have to cut part way through and bend it to see if the grain is there.

 

Wrought iron isn't, imo, better or worse than modern steel for forging.  Because you can't usually get it in the size you want, you have to burn a lot of fuel to reshape the stock.  If the piece you're making doesn't need the grain pattern exposed for appearance sake, working with mild steel is far quicker and easier.

Good wrought iron can be very nice to forge but tires are usually made from pretty crappy wrought and need quite a bit of forging before they start to behave.

tell me is a corvette a better vehicle than a dump truck?  Oh yes I'm not going to tell you if it needs to haul 5 tons of gravel or win road races...

 

Wrought iron is great for some things an lousy for others---just like modern mild steel.

 

On the whole WI is a bit harder to learn to forge with.  It's greatest utility is for historical reproductions IMNSHO

Wrought iron comes in different grades, levels of refinement.  High grade wrought iron forges beautifully like butter.  Low grade wrought iron forges like a rotten piece of wood.  Like Jim said, tires tend to be of a lower grade/quality wrought iron.

Also they tend to go high at antique stores, last one I bought was US$5 at the scrapyard