Standardbreds are the nicest best horses I've ever had!! Standardbreds are pacers and trotter, not gaited so it's a bit harder to teach them and they have huge strides and you need an outstanding seat to ride that breed! But they're amazing jumpers and they're so sweet and caring never, a foot out of place! Tb's can be high strung but they're easier to train and they're better for equitation and more popular. They move better then sb's because it's natural as pacing would be natural for a standardbred. Honestly just adopt the horse that is perfect for you! Who really cares about the breed?? Good luck!!
Tb's are much more common in the hunter/jumper world. Make sure to vet check ottb's and check tattoos on the jockey club website. When it comes to age, experience, and past injuries it's always better to see for yourself. They can be fantastic sport horses