Help and advice ...

Show the builder the specs on that first computer then what the second has and tell him what you expected.

Here are a couple of links for you to compare what you have. Your first computer has a tri-core and distinct graphics while your second has a dual core with Radeon(tm) HD Graphics GPU integrated on the CPU.

This link shows your SECOND systems Passmark CPU mark of 2126 (higher numbers are better)
http://www.cpubenchmark.net/cpu.php?cpu=AMD+A6-5400K+APU

This link shows your FIRST systems Passmark CPU Mark of 2592 and if you continue to scroll down the page 59 items lower you will spot the APU from your second system.
http://www.cpubenchmark.net/cpu_lookup.php?cpu=AMD+Athlon+II+X3+450&id=159

As Bob tried to tell you, it looks loke your builder is using what he can find cheap and not trying to give you an exact match but rather just something roughly comparable.

As someone else stated, NEITHER of your systems is configured as an actual gaming system although both will allow you to play some games ok and others not as well.

The time to ask is BEFORE having a system built rather than afterwards as unless you actually have the desired specs IN WRITING the builder isn't really required to start trading parts.

The advise, if what you wanted built is in writing, is to show him that the two computers are not a matched pair and to make them that way.