I think the biggest difference is that transistor cards are solid-state where relay cards are not.
A couple of difference I have noticed are that transistor cards have a lower ampacity rating, they are almost always one single voltage per card, they cause less noise (AB relay cards are bad for this) and they don't burn out nearly as often as relay cards.
Relay cards do have advantages such as you can mix voltages on a card and they can switch higher levels of current.
THese are just my own observations working with AB SLC series plcs. Other manufacturers might be different.