Tick/volume/range bar charts are more sensitive to actual price action and trading, so they might give a better representation of what's going on currently.
I'm not quite sure what you mean by "sensitive to price action and trading", but I certainly agree that they give you a better representation of what's going on than timed charts do. (There's nothing to stop you from looking at both/all three, if you want to?).
For what it's worth (if anything) if you're looking at changing how your charts are constructed, personally I'd strongly recommend constant-volume bars over tick charts. My reservations about tick charts include my perception that, unlike volume charts, they don't/can't distinguish between tiny and huge orders being transacted.
I have done quite a bit of experimentation with all three charts mentioned above, but I have yet to find a significant edge over time based charts.
It's not easy to verify. It requires meticulous, methodical research and analysis over a long period.
I'd been increasingly strongly advised to switch to volume charts by (successful, professional) traders I knew, who knew how I traded. I eventually tried it, and ended up wishing I'd done so at an earlier stage (but I'm very difficult to teach/advise and have to work almost everything out for myself). I effectively ran both methods (i.e. timed and volume charts) side-by-side for 6 months, taking "the same" price-action-based entries for each, with the same trade management (different trades, of course, though not very different numbers of trades, overall), and compared the results, which were consistently and significantly favourable for futures/volume: briefly, I was able to average about 25% more profit, overall, without increasing the risk, each month for 6 consecutive months. This is, of course, a very superficial, abbreviated summary - the statistical analysis was much more complicated and intricate than I'm making it sound; but the mechanics of actually doing it weren't.
I assume most people using price driven charts are day traders anyway.
Again, with apologies, I'm not quite clear what you mean by "price-driven charts", here. What sort of charts aren't "price-driven"?