Adding to Verber's liquid vs. solid comparison, the solid tablets have a higher concentration of chlorine dioxide -- which also explains the heavier swimming pool taste. Personally, I can't stand the taste and won't use either. However, some people can't tell the taste while others swear the chemicals make the water taste better! YMMV.
Taste aside, there is something to be said for Micropur chlorine dioxide tablets over the Aqua Mira liquids. Micropur's higher efficacy allows it to be marketed as effective against bacteria, protozoa, and viruses. Aqua Mira's lower concentration of the same active ingredient allows it only to mention effectivness against bacteria! Just last year, Aqua Mira finally came out with its own tablet version.
In the end (not that I am an expert), my hunch is that they're both sufficiently effective -- but if I were to choose, I would choose the tablets -- to eliminate the annoyance of counting, mixing solution drops and then having to wait the extra five minutes before pouring the mixed solution into your water. With tablets, you just drop in one tablet per liter and that's it. Once the chemicals are in your water, that's when treatment time begins: 20 minutes most of the time, but longer if water is cold -- up to a 4 HOUR wait if your water is just above freezing.
Sucking chorine-dioxide treated water through a filter (e.g. Frontier) does have two important advantages:
1. Your filter can remove the swimming pool taste -- if that matters to you.
2. Your filter can improve water clarity -- some folks just don't want to drink brown river water, even if treated.
3. The up to 4-HOUR treatment time for very cold water is really to kill the bigger stuff -- like protozoa. If you use a filter, then 20 minutes should be enough to kill bacteria and viruses even in very cold water -- and your filter can block the bigger, harder to kill stuff. Let each tool do what it does best.