I agree the original anime is superb. I preferred that strength rarely determined the outcome of the fight too and if so, there was a whole adventure Goku had to go on to become stronger, like finding the super divine water for example. Also, as it's the start of the journey, the characterisation is superior.
Originally there was no division between Dragon Ball & Z in the manga though. The only reason Z exists on it's own was for marketing reasons and to highlight the shift in tone between the two. It just depends what your preferences are. Z is really good also, but it follows the more traditional Shōnen story route, with its heavy action & transformations, as opposed to the light-hearted nature of the original.
Are you watching the original Dragon Ball Z or Kai? Kai cuts out the filler and gets straight to the action, which personally i'm not a big fan of. The fillers contain a lot of the humour and easy-going stories which are similar to the original Dragon Ball.