Hello!
When it comes to 2k3 and Rise, I love all the turts very dearly. I just tend to fixate on my top blorbos, haha.
I assume you're specifically asking about the 2k3 turtles, so I'll talk about them! When thinking about Leo and Raph's relationship, this extract from Leo's bio usually comes to my mind.
(Transcription: While I often disagree with Raphael, he is my brother, and I enjoy the times that we spend goofing off. I just wish that he'd try to see things from some other perspective than his own (something he no doubt says about me as well!))
I think it was originally showcased on some official 2k3 tmnt website. You can read the whole thing here.
I'm super fond of this bit, because I think it sums them up very well. It's just very down-to-earth and peaceful sentiment. Leo acknowledges that yes, Raph can frustrate him a lot, but he loves him and spending time with him anyway.
AND the "something he no doubt says about me as well!" Has kind of stuck with me since the first time I saw it. Leo's like; "Yeah, I get it. I can be a pain in the shell too." And I don't think he vocalizes this sentiment, in these kind of terms in the show.
The 1st season sets up a lot of Leo vs Raph rivalry, with Leo being the responsible one and Raph rebelling against that. They have the big clash in 2nd season City at War arc. In SAINW universe they're basically on "It's On Sight(however impaired)" -terms. The 2007 movie with it's Leo&Raph drama often bleeds into 2k3 fanworks. So I get where the fanon interpretation of them hating each other comes from. I just feel like it often gets blown out of proportion. Most of the time those two get along well and rely on each other.
And since you asked how I feel about the other turtles, I'll try to summarize here what I love about them, haha!
I adore 2003 Raph, because he's so damn hilarious. The gruffiness, deadpan sass, feral troublemaking, the " oh for FUCK'S SAKE!!" -energy. He has this special flavor of being so done with everything, all the time. It's so funny. And then there's his calmer side. When he's mature and reliable, a fierce protector <3.
2003 Donnie is hands down my favorite Donnie ever. His gentle, soft-spoken nature, patience and kindness are so special. He's such a sweetheart! A silly boy! But he won't let you walk over him! He'll sass and shoot you with a lazergun!
I'm a huge fan of 2003 Mikey's portrayal. Because he's the classic fun-loving imp, who loves to cause trouble and goof around, but he's also very down-to-earth. He's really resilient, competent and mature when the situation calls for it. Despite his own dramatics and his brothers often teasing him, he feels trusted and respected.
Overall I appreciate how well written the turtles are in 2k3. They are very grounded, complex and multidimensional, with a lot of depth to them. And the way you get so many different dynamics with different brother combos, is endlessly fascinating.
Anyway's hope you enjoyed my ramblings. Thanks for the ask!