As a pet meter an AlphaTRak will read higher than the Freestyle Lite human meter. ALL human meters will read lower than a pet meter but the difference is much smaller at low BGs and significantly larger at high BGs. The problem is the cost of AlphaTrak test strips. If that's not an obstacle for you, get the AlphaTrak. Your vet will prefer it. The Freestyle Lite is a great meter - needs only a tiny drop, reads fast, almost never gives an error message, etc. It's known to read on the low side so this has to be taken into account if you use it. It's the meter I use.
Most of us here eventually go to a human meter because using an AT meter is too darned expensive. You have to wrap your head around using a meter to get a sense of the BG patterns rather than worrying about whether it's exactly the right BG reading. All the dosing advice given here includes human meter guidelines. Basically you need to know what's too high, OK and too low on your particular meter. That's it.
Once you decide on a meter, work with that meter only. Don't have two meters and do constant side by side comparisons - it'll make you crazy. If your vet insists on looking only at AT meter numbers buy one for vet curves and buy a cheaper to use human meter day for to day.