I have a 3. The problems with animations and frame rates exist on my iPad Air and iPhone 5S. The trouble with effects is the OS, not the hardware.
The 3 is a great device and was in the OP's price range. I guess recommending a device they can afford is "abysmal advice"
No no, don't try to turn it round. You said that there was nothing between the 3 and 4, which IS abysmal advice. The 3 has no life left in it, it is done. The performance leap from the 3 to the 4 thanks to the A6X is huge when running power hungry apps. On iOS 6 the iPad 3 was fine, the OS was smooth but on iOS 7 it is below par. The "iOS 7" frame drops seen on all devices (pre 7.1 may I add) are on all devices but I'm talking simple UI performance, where the iPad 3 has stutters and frame drops where the other devices do not. Hate to tell you, my wife now has my 3 and on iOS 7 it's horrible compared to my 4. I've done side by side comparisons. If you do have an iPad Air you would know this yourself.
Recommending a device that is already struggling on the new OS and will likely either not get iOS 8 or run even slower if it does receive iOS 8 is NOT good advice. On iOS 7 the 4 is closer to the Air in UI performance where there IS very little between those two (right now, but that will change in the next 6-8 months) and all current power apps run near identical to how they do on the Air (see Space Hulk, Infinity Blade 3, Xcom, etc).
Load times on apps like iPhoto and iMovie are slower, games like (the relatively old) NOVA 3 allow either high resolution or full effects but not both at the same time. Most other games are stripped of some graphical effects as seen on the likes of NFS Most Wanted. The A5X is not powerful enough to drive high performance apps on that Retina Display and it sure can't handle iOS 7 even with the transparency effects disabled.
The iPad 4 can be found either second hand or on the refurb store for great prices. And while yes it is more expensive than the 3, that little extra now will gain another year or so of proper, good performance use.
So no you weren't recommend a device within budget, you were recommending a tablet that would have been more or less DOA for the guy and given him a below par first impression of the iPad due to poor performance.
Anyone recommending an iPad 3 in the iOS 7 era with cheaper refurb iPad 4's around IS giving abysmal advice. And again saying there's "not much" between the 3 and 4 is just so factually wrong ... and sounds more like self pacification than anything else.