At the first sight they really look quite similar. Counter does not use a relational database and is highly optimized to serve users for free. If you want more details and really dig into the data plausible could be a better fit. If you value a free product and don't need too much details or actually even value less data collection then I would say go with counter.
If you're collecting data, you generally want a) as much as you can get and b) be able to make use of it any way you want.
Yes users of a privacy centric analytics tool are opting into less information, though the inability to do more may be a large downside to counter (if it is the case that it has less data collection capabilities vs plausible at this time). You never know what data you will need later, better to collect however much you're able to in a fashion you can do anything you need to with it.
