My opinion is similar to Conchita’s: “agree something” is probably mainly British and “agree on something” is more common.
But I question whether you can say “agree the new prices”. If you say “the”, wouldn’t that usually indicate that the prices had already been previously determined (by someone else)? In that case you’d have to say “We agreed to the new prices”.
But “agree new prices” or “agree on new prices” AND “agree a new price” or “agree on a new price” would be OK.
I also think “agree something” would be used mainly to talk about things such as a treaty, a contract, a policy, etc. In other words, something fairly formal or businesslike.
“We agreed a new five-year contract.” (*BE)
“My husband and I finally agreed on a name for the baby.”
One last comment (my gut feeling ;)):
The sentence “We agreed a new five-year contract.” would be mainly a British usage. Americans would probably be more likely to say “We negotiated a new five-year contract.” (i.e., the word “agree” might not be used at all.)