I prefer the TASCAM - but I have limited experience with ADATs, so I wouldn't be the best judge. I just plain don't care for a lot of Alesis' gear.
DA-88's were the standard in most post-production houses. I don't know if they ever got the "industry standard" tag in most recording studios - but I know they were popular in the post-production environment because of their syncability (hey, did I just make a new word?) with each other and to external sources (i.e. video, film). Many other reasons, I am sure.
I think now, you will still find a lot of them in studios and post-production houses because they are workhorses and have a reputation. I think "industry standard" is changing to the new technology (hard disk systems). I can speak for one post house that I know of that has a whole new hard disk system, but they held on to their wall of 88's just in case.
For the record, I use the 88's little brother - I have a pair of DA-38's. Same thing basically, with some improvements in some areas, and not so many bells & whistles.
TASCAM also has newer versions based on the ol' 88. The DA-78 and I think a DA-98 as well.