What halachic advantages are there in purchasing tekhelet strings dyed by the murex snail as opposed to tekhelet strings dyed by the cuttlefish?
Are Radziner cuttlefish-dyed strings acceptable?
That question is answered very well on YouTube "Radziner Vs. Murex Tekheleth, The Truth!". Murex is Argaman not techalet. Buy the cheaper and go Darg or cuttlefish. A snail is not a fish or does not swim or have fins. So the Radzinger version is obviously right, but watch the Youtube. This is a good comparison. http://www.techelet.info/chilazon-comparison/
This video presents the results of many years of unbiased research by Mori (Rabbi) Michael S. Bar-Ron, championing the kashruth of Radziner tekheleth over Murex tekheleth (Argaman). https://www.youtube.com/watch?v=zKhbhTkrGtQ
To the best of my understanding there is archaeological evidence proving the use of the murex trunculus as an ancient dye, particularly in Israel, because of an ancient murex-dyeing site unearthed near the Temple Mount and an ancient textiled that contains a murex-dyed blue stripe found near Masada.
I need a source for this also (can someone help out) but I seem to recall a Gemara or something that mentions the Romans outlawed the use of techeiles by anyone but royalty, and the Romans commonly used the murex trunculus snail, not the cuttlefish, to dye blue clothing.
Like everyone else who has answered this question, I strongly recommend watching this YouTube video explaining why the Radziner-cuttlefish method for dyeing techeiles is more authentic.
And, truth be told, it could very well be that cuttlefish and murex snails are both not the chilazon.
But there is sufficient proof that the cuttlefish is the chilazon, and if you honestly believe that then Radziner techeiles is perfectly acceptable for you.