HeartGold and SoulSilver were better than Black and White. I'm not trying to be a nostalgiafag, but HeartGold and SoulSilver were just better disregarding the Pokemon themselves and their designs (as that doesn't matter).
HG/SS starts out with a goal: go to Mr. Pokemon's house and grab an egg. Simple, yes, but it does help you know what to do. In B/W, Juniper's just like "FOLLOW MEEEEEEEEEEEEEEEEE", which isn't as effective in grabbing one's attention.
HG/SS's rival is this asshole who you feel motivated to stop, as he stole Elm's Pokemon. B/W's rivals are annoying "friends". There's the dopey Bianca, who couldn't battle her way out of a paper bag, and Cheren, who craves POWER. Cheren is cold and calculating, but doesn't do anything to make you hate him, unlike Silver, Blue or even Barry. Instead of saying "this asshole's gonna get it now", I was saying "UGH NOT THESE GUYS AGAIN". The fact that they're EVERYWHERE doesn't help.
B/W's Team Plasma is better than HG/SS's Team Rocket, but both were interesting. I'd say each does what GameFreak were going for well. However, B/W does give a good excuse to need to catch/defeat the main legendary, whereas HG/SS just forces you to for no good reason.
The Elite Four of B/W and HG/SS are about even, both with disappointing champions, but good otherwise.
Postgame-wise, HG/SS shits all over B/W, with an extra region and fucking Red. B/W's postgame isn't bad, but it's just useless towns and trainers with high-level Pokemon for no reason. HG/SS at least tried to ease into the rematches against gym leaders/E4 with level 60s/70s.
Oh, and HG/SS had rematches against gym leaders. B/W didn't.
B/W replaced contests with musicals. The musicals' only rewards are more items for the musicals. HG/SS had the Pokeathelon, which allowed you to get evolution stones and other nice items.
B/W's gyms were really imaginative, but a bit annoying to traverse (apart from the first two). HG/SS had a few creative gyms, but mostly played it safe. I like both for what they are.
Interface-wise, HG/SS keeps everything on the bottom of the screen, with togglable running shoes, which is VERY convenient. B/W just has the useless C-Gear, which I haven't even used. B/W's C-Gear is a step back from D/P/P's Poketch, which is wholly useless compared to HG/SS's bottom screen menu.
As far as aesthetics goes, B/W's graphics are technically better, but the games go to great lengths to shove them down your throat with the fifteen bridges and a few cutscenes. HG/SS lets you admire the scenery at your own pace, or not at all.
B/W has fully-animated Pokemon sprites, but I'd trade them in an instant for HG/SS's following Pokemon. Both are just aesthetic, for the most part, but HG/SS made me feel more like I was on this journey with my Pokemon.
So, all in all, I'd say HG/SS were better games than B/W. Not that B/W were bad, but HG/SS were the pinnacle of Pokemon gameplay. Sure, Johto and Kanto don't have a desert or an electric cave or changing seasons, but the gameplay takes precedence over the technology, which is definitely a good thing.