Tomorrow I'm closing on an older home with a detached garage, the door has extension springs which are attached to the door and pulleys by chains instead of the cables used today. Would it be best to replace the chains with cables or are the older style chains the better system? The extension springs are toast so I will definitely replace them.

Chain is fine.

I have worked for two different door company's and have never seen a door with chains instead of cables. Would you mind posting a picture of your door?

Have you considered simply replacing the whole door? My parents had their replaced last year with an insulated door for $1,800 installed with a new opener. An uninsulated one was like $1,200 - $1,400 installed.

I've considered it but it's not in the budget right now, I just bought the house and moved in last week so I have other expenses that come first.

There is nothing wrong with correctly sized chains.
New springs and you should be good to go.

The springs were rusted so bad I couldn't tell what color they were marked with, I thought I could make out a touch of blue so I replaced them with 140lb springs and the garage is still pretty hard to open.

Why did you move in before you closed on the home?

He didn't. Last Mon. he started the thread saying he was closing that week. This week, he said he bought (closed) and moved in last week.

Not that it matters, and has nothing to do with my questions...but I closed on the 10th and started moving in that day hence the original post from the 9th stating I close tomorrow.

chains are alright

The only way to match springs, new to old,  measure inner diameter of spring coil, measure length of collapsed coil, measure coils per inch, and maybe diameter of wire the coil is made.  If the old ones are the wrong size then you have to weigh the door.

http://ddmgaragedoors.com/springs/sectional-garage-door-extension-springs.php

I dont know if ive purchased springs from this company but I like their calculator. The layout looks different from when I had to replace torsion springs recently that where broke and mismatched sized.

If the door is still hard to open, check the cable pulleys and track wheels.  A few bad bearings really add resistance when opening.  Also might check the track.  When my torsion spring blew apart, it twisted the track out of alignment.

If possible run a cable through the spring as a saftey.  I see what looks like one in the top pic but it doesn't appear to attach to the wall on the door end.