The original movie did a fantastic job of streamlining the story into an almost mano-a-mano showdown without sacrificing any supporting characters, who indeed are much more vividly realized and rotate throughout the film very effectively with their eclectic personalities. Scott's remake attempts the same thing, but we never really get to know many of the characters and, the ones we do, we don't really get invested in. That's a pretty crucial aspect for a film about hostages. Even the supporting terrorists are kind of anonymous gunmen in the new version.
Let's be fair about this, though, and take the original out of the equation to eliminate any unfair comparisons and judge Scott's remake as a stand alone piece. One may be more sympathetic to its shortcomings if they're unaware it had been done before (and successfully). This is not a shot-for-shot remake and there are a tremendous amount of changes, but they hinder the film more than they help it.
One example is John Travolta's role as the lead villain. It's very oddly written and even more oddly performed. He's clearly a psychopath, but he (the character, I mean) is performing for the sake of misdirection. The hijacking scheme is a smokescreen for manipulating the market. So, “Ryder” (as he's called in the film) is not only conning law enforcement, he's also conning his cohorts. Consequently, the audience is uncertain as to what kind of bad guy this really is. He seems to really delight in killing his hostages, but he blames their deaths on everyone other than him. He goes from laughing and treating the matter very nonchalantly to flying into fits of rage like a child throwing a tantrum. Also, he's an investment banker who kills people. I'm sure that's not outside of the realm of possibility, but it feels odd here, because with his handlebar mustache, neck tattoos, and scrappy clothes, he looks and acts more like a violent criminal than a white collar one. You don't have to compare his character to Robert Shaw's in order to spot the flaws.
These, of course, are mostly complaints about the writing, not the directing. So, how does Tony Scott do in the telling this (flawed) story? It's certainly watchable. And, even though it's largely forgettable, it is still entertaining for the most part. I think the biggest criticism I have about Scott's direction here is that it feels a bit like a paycheck project that he just phoned in. Not much of his usual nuance or, for that matter, joy comes across. Consider “The Last Boy Scout.” That was a film that it's rumored made everyone involved with it miserable throughout its production. Yet, for whatever reason, it transcends its difficulties and feels like a joyride. For all I know, “The Taking of Pelham 123” was great fun to make. It doesn't feel like it, though. In fact, this is possibly Tony Scott's weakest film. Unfortunately, it's not just because it's a remake.