I’d say a normal phone is a lot worse than smartphones in general, unless you don’t care about all your communications being readable by the carrier. With a smartphone you can make actually encrypted calls and texts over trustworthy applications/protocols (Signal, Matrix, Simplex, etc.), on a phone you’re stuck with the carrier service; another thing that comes to mind is the storage, as far as I know there are no normal phones with an encrypted filesystem while it is default for a long while on Android.
On the other hand, if your new smartphone model isn’t loaded with a privacy respecting ROM you’ll also have at least some data sent to other third parties like Google and whatnot, but if you can change the ROM, then the potential for better privacy far outweighs the benefits of normal phones doing fewer things with your data by default. If you’re going to use your new smartphone like an old phone, to make carrier calls and SMS, then there will be near to no improvements (except storage security maybe) and as you say, more data snooping