Oh yeah. Stannis and Dany have a surprising amount of similarities actually, which is partially why I believe they are the two initial power player rulers still alive (an argument could be made for Cersei, but she was never the main monarch since she derived her power from others as well as having been displaced for over a book now.)
Dany and Stannis are both proud, stubborn, and duty driven. Dany and Stannis both have a huge sense of obligation to their subjects and obligation to their heritage. They both fall to rather reluctant rulers compared to many who stay in the game out of a sense of responsibility. They see it more as a right rather than a desire; they are both actually not all too power hungry compared to other rulers.
There’s a definite parallel in my mind to be drawn here:
“Enough.” Dany slapped the table. “No one will be left to die. You are all my people.” Her dreams of home and love had blinded her. “I will not abandon Meereen to the fate of Astapor. It grieves me to say so, but Westeros must wait.”
Dany does what she feels is right for the people, her people, rather than attempt to continue her quest for the Iron Throne. This is not unlike Stannis, aka “the king who still cared”.
Few of the birds that Aemon had sent off had returned as yet. One reached Stannis, though. One found Dragonstone, and a king who still cared. Sam, ASoS
“Words. Words are wind. Why do you think I abandoned Dragonstone and sailed to the Wall, Lord Snow?”
“I am no lord, sire. You came because we sent for you, I hope. Though I could not say why you took so long about it,”
Surprisingly, Stannis smiled at that. “You’re bold enough to be a Stark. Yes, I should have come sooner. If not for my Hand, I might not have come at all. Lord Seaworth is a man of humble birth, but he reminded me of my duty, when all I could think of was my rights. I had the cart before the horse, Davos said. I was trying to win the throne to save the kingdom, when I should have been trying to save the kingdom to win the throne.” Jon, ASoS
Also, Dany unheard of intervention when her people (the Dothraki) are raping people in AGoT is very unusual. Most ASoIaF leaders can’t/don’t/won’t keep their people from enjoying their conquest with raping and other misdeeds. But Stannis is another exception:
"King Stannis keeps his men well in hand, that’s plain. He lets them plunder some, but I’ve only heard of three wildling women being raped, and the men who did it have all been gelded." Samwell, ASoS
Keep in mind that- as we saw with Arya’s ASoS POV- this was 100% not the case with Robb and the Stark campaign. It’s unusual like I said to prohibit such actions and justly punish the men who ignore the order.
There’s also the fact that both Dany and Stannis have a very stubborn refusal to acknowledge the benefits of lining up or forgiving those that they believe have done them injustice. Stannis takes a hard stance against joining up with “usurpers” like Robb Stark for the sake of winning the war and displacing the Lannisters, he ignores the logic of that course for the sake of his beliefs. Dany has a somewhat similar approach to lumping all the “Usurper’s dogs” together the way Stannis lumped all “usurpers” together period despite the irrational nature (and problematic/detrimental aspects) of such groupings.
“Have you forgotten Princess Rhaenys and Prince Aegon?”
“Never. That was Lannister work, Your Grace.”
“Lannister or Stark, what difference? Viserys used to call them the Usurper’s dogs. If a child is set upon by a pack of hounds, does it matter which one tears out his throat? All the dogs are just as guilty.” Dany, ADWD
“As you intend to sail, it is vital that you make common cause with Lord Stark and Lady Arryn…
“I make common cause with no one,” Stannis Baratheon said.
“No more than light makes common cause with darkness.” Lady Selyse took his hand.
Stannis nodded. “The Starks seek to steal half my kingdom, even as the Lannisters have stolen my throne and my own sweet brother the swords and service and strongholds that are mine by rights. They are all usurpers, and they are all my enemies.” Cressen, ACoK
Another parallel that I find interesting about them, too, is their complex relationships with their younger of two brothers (Renly and Viserys.) In some respects, one more than other, both were somewhat involved in the death of their brother- after being betrayed by them. However, they derive no pleasure from their deaths and prefer to think of them as how they were before they betrayed them.
“What do the smallfolk say of Renly’s death? “
“They grieve. Your brother was well loved.”
“Fools love a fool,” grumbled Stannis, “but I grieve for him as well. For the boy he was, not the man he grew to be.”
…“Only Renly could vex me so with a piece of fruit. He brought his doom on himself with his treason, but I did love him, Davos. I know that now. I swear, I will go to my grave thinking of my brother’s peach.” Davos, ACoK
Viserys had been stupid and vicious, she had come to realize, yet sometimes she missed him all the same. Not the cruel weak man he had become by the end, but the brother who had sometimes let her creep into his bed, the boy who told her tales of the Seven Kingdoms, and talked of how much better their lives would be once he claimed his crown. Dany, ASoS
(to a hallucination of Viserys) “You are dead,” Dany said.
Murdered. Though his lips never moved, somehow she could hear his voice, whispering in her ear. You never mourned me, sister. It is hard to die unmourned.
“I loved you once.”Dany, ADWD
So both of them actually have similar relationships to these siblings. Stannis and Dany loved their brothers and mourn them, but they also only truly miss the “boy” the once were rather than the “man” they became.
There are plenty more I think, but here’s a few. Basically, I actually think Dany and Stannis have quite a few similarities.