What are desirable planeswalker characteristics?
In general, Planeswalkers are slow to do anything by themselves, so the ones that see tournament play are the ones whose early abilities complement the deck or give immediate card advantage.

Gideon, Champion of Justice

Gideon takes about 4 turns to get out (by mana cost). His +1 doesn't do anything useful immediately, and even when he does get big he can be stopped by 1 chump blocker a turn. His ultimate is good, and will probably win you the game, but it takes a long time to activate and it puts all of your eggs in one basket, making you very vulnerable to a Swords to Plowshares

Vraska the Unseen

Vraska, again, probably doesn't get out until turn 5. Her +1 ability does nothing but deter your opponent from going after Vraska, which does nothing to stop them from killing you. Her -3 is useful, but half of her loyalty is a bit of a steep price to pay to destroy just one permanent. And her ultimate, which you're optimistically getting off on turn 8, does nothing if your opponent has 3 bears to block with.

Domri Rade

Domri, on the other hand, gets out on turn 3 and immediately starts helping you get cards. With him on the field in a creature heavy deck, you are much more likely to be able to play a creature every single turn. And if you do manage to get his ultimate off, then the double strike+trample combo makes even a few moderate powered creatures into a major threat.

Jace, Architect of Thought

Jace, like Gideon, gets out on turn 4. However, his +1 ability immediately protects both you and him by weakening your opponent's creatures, and generally just slows them down, which is very useful for a control player. His -2 ability is also one of the best effects in the game (consider that it's strictly better than "Reveal the top 3 cards of your library. Put 1 into your hand and the rest on bottom in any order"). His ultimate is very situational, but you don't really need it when the other abilities are doing so much for you.

Conclusion

Domri and Jace share two major qualities. First, they complement existing major deck archetypes: Domri accelerates a Red/Green aggro deck, and Jace helps a mono Blue control deck both by slowing the opponent down and by getting the player the cards they need when they need them. Second, they both give the player card advantage. Getting more cards into your hand from your library every turn is very useful both because it helps you play more quickly by making it more likely that you'll hit land drops and have cards to play, and because it makes it more likely that you'll have the cards you need when you need them.