Like, I don't understand why people are excited about secret bases I guess. Yay a room I can decorate. Big woop? This was in the Sinnoh underground too and no one liked it then (when you could have traps etc to stop people getting in). What made the RSE ones so much better exactly? :|
Well... for a start, the bases were located in the overworld. That meant, you could take your most favourite little spot in Hoenn and claim it as your own, so to say. Whether you chose an indent in the wall south of Rusturf Tunnel, a pile of leaves north of the Weather Institute or a tree on the secret beach north of Rustboro, your base was visible in the overworld, and you could see the entrance to your little base when you travelled around. You could also mix records with friends and have a wild little hunt for their base. There are a few surprisingly good hiding spots littered across Hoenn.
Contrast Sinnoh, where your base will always be an anonymous hole in an anonymous wall in an anonymous tunnel deep below Sinnoh. Instead of claiming a special little corner of the overworld for yourself, you could drill into any one wall in the featureless, empty tunnel network below the region. Any wall would do, they were all exactly the same.
Also note that for the most part, Hoenn's bases gave you full access to the entire area as soon as you entered the base. In Sinnoh, you had to link with your friends to clear away rocks from your base, so they wouldn't be in the way when you built. Highly disruptive and annoying, especially when you tried to place big decorations (but were unable to because you hadn't linked with enough friends).
Sinnoh separated the bases from the rest of the game too much. In the overworld, there was no talk of bases, decorations or other items from the Underground. Hoenn had many people talking about the bases, you could buy furniture and other decorations for them in several different places, and if you mixed records, you were likely to bump into a friend's base somewhere along your adventure. Secret Bases felt like an integrated part of Hoenn, whereas in Sinnoh, they felt tacked on to the Underground sidegame, and you were given way more limitations than opportunities for them.
Never mind that you could battle your friends' Pokémon and actually gain experience from them. In a game where the highest-levelled opponent you can beat regularly is at level 58, this feels like a godsend. Grinding the Elite Four for opposing Pokémon in the mid-fifties isn't actually fun in the long run, such as when you try to get a 'mon to lvl 100.