It all comes down to what you want to get out of the instrument. I know that's a broad statement but it's also the easiest way to answer your question. Depending on what you want to do will determine if you're limited or not. If you can, learn both to the extent you'd like to learn. You're already making the step towards finding any pros and cons regarding each technique but ultimately, do what feels comfortable to you to do - not what the most opinionated bassist may convince you to feel. Yes, technically, not using a pick will allow you to do "more" but both techniques of their own beneficial dynamics. Try not to differentiate both as individual techniques. Try to see them as individual dynamics that you can apply to your arsenal.
That's my advice, whether you find it useful or not. I speak from experience not as a fellow bassist but as a guitarist who sees the benefit in both techniques. SRV, Jody Fisher, Steve Vai, Brad Paisley, Paco de Lucia, Buckethead. (Yes, Brad Paisley is one hell of a guitarist) This list isn't even remotely close to the tip of the iceburg with unique technique on guitar leveraging methods of using a pick and using fingers on the the right hand. I know the same types of comparisons can be drawn for bassists as well, so try to see it in terms other than one or the other! If you dig one more than the other, then that's great! If you like both, then attempt both! The greatest thing of all is that you'll always have the option to do whatever you choose.
I wish you the best of luck with your quest as a musician!
-Stephen
