I will be moving about 450 miles. Is it cheaper to move old usable
furniture like chairs, tables, sofas or buy moderately priced
replacements in the new city?  Is there a formula or a percentage?  My
furniture is in good shape but I am not overly fond of some of it. 
How can I estimate the rough comparative cost of moving or buying?

Pay $30-40 to put your stuff into storage for one month (or, leave it
with a friend). Move, then check out the local deals, esp. in thrift
stores.

Why are you worried about percentages and formulas? You must be one of
those fancy, edumacated city folk.

You might compromise, taking the furniture you like in a U-Haul
trailer or rental truck/van (cheaper than movers), and replace the
things you aren't fond of.