Champs you miss the most, champs you don't
I miss: I think old Malzahar tops it for me. It felt great when you learned how to combo and during teamfights if you didn't combo someone down you could still be very helpful with zoning the enemy team so long as you had Rylai's. And jungle AD Malz was hysterically fun. New Malzahar feels completely braindead. Like, he's still good. Just one dimensional and not very fun to play.
Then there's old Kayle who was the quintessential hybrid champ... whose build was expensive but became a monster late game. Even her first rework where she became more of a team resistances shredder but had that oppressive early game with sheen was more fun than she is now.
Old Ryze where he was a short-ranged mage/assassin was way more fun than the bloated and convoluted kit that's just like a mockery of Brand's kit he has now and more fun than the tank-Ryze they had him as before that.
Oldlaf when nobody really played him but he was just this amazing powerhouse that flew under the radar.
Old Veigar... to be honest I mostly miss his insta-stun. If you had some skill with it, you could insta-stun half the enemy team or more by catching them all on the edge. It was amazing and saved me from so many bad teamfights or early tower dives when people didn't realize it was off cd.
Old old Katarina. When you carried you felt like you could 1v5 (so long as they didn't have hard cc, which used to be pretty common back then) and when you failed ya failed hard... but man if she wasn't one of the most fun champions to play. She's possibly stronger now in her current iteration but it feels like her kit was more designed for "LCS BIG PLAYS!!!" rather than just having a really nice flow to all her skills.
Rounding it out would be the first champ I felt completely betrayed about when they changed them... which was old moneybags GP. I literally learned how to farm and last hit by playing him. Getting that ultimate Q shot on the carry was the dream, and made you feel good about one of the very basic mechanics of the game. Plus he was way more piratey fun than "serious brooding emo pirate".
I don't miss:
Old Nasus. Man, he was literally the worst. Had an attractive farming based kit like old GP, but just got torn up by every new top champion after Renekton got his first buff and getting kited was the worst feeling (it still is but new wither and his other changes helps so much).
Old Yorick. Just a disaster all around. Kind of fun to play, especially when going non-meta like support Yorick... but wow what an awful kit he had. So glad they changed him.
Old Garen. Never. Facecheck. Ever. Fear the bushes. All game long. Even if you're just going to ward. Don't.
Old Xin Zhao. Basically the same as old Garen. Also, he was an all-in champ with awkward builds at the time.
Old Jarvan. You will lose if playing against, and win if playing with. Just incredibly strong at all phases of the game. Now he feels more balanced.

. Back when her e burned you for like half your hp if you were a mage.