I like the grey the best, but in the video his trot looks either restricted or like he is off in the hind end.
I like the standardbred, but I would look at him moving freely if you can because his canter in his dressage test looked odd to me. I also agree that if they say antsy, it can mean fruity, so look into that.
Based on things the rider does with her, I would be willing to bet that the tbx needs more schooling than they are letting on, or they have rushed her and left holes. In both canter videos, you can see the rider have to set her up very deliberately with wide low hands to ask for the lead.