Is GBA "emulation" on DSi really THAT bad?

I'm currently with the opton of buying either a DS Lite or a DSi for the same price. Both come with a R4 Flash Card.

I want to use the DS mainly to Play DS and GBA games, and I know DSii has overall better hardware, more RAM etc, but I keep reading that gbarunner2 is terrible because it's more of an emulator than native (not really, but not native)

I also learned that the DS Lite can run GBA games natively using Twilight Menu on a R4 so you don't even need to buy a expensive GBA EZ Flash.

I'm not a purist or anything like that, but I would like to play all of the good GBA games. Buying original GBA games in my country is not worth it at all (too damn expensive) so that's out of the question (so the actual GBA socket on the DS Lite would not have any use for me), but I'd like to play my GBA backups on twlight menu and not run into a ton of erros.

That said, should I buy a DS Lite instead of a DSi just because of the hardware? Even tho I won't be physically using a GBA Cartridge on DS Lite's GBA socket?