The best short assessment of Tony Blair I've seen is this one by Geoffrey Wheatcroft in Slate.com. Wheatcroft thinks the British peoples' disappointment (and much worse) in Tony Blair has to do with more than the Iraq war. There was a disparity throughout his career between words and deeds. He promised to be squeaky-clean and presided over scandal and corrupti0n, and so on.
He may have been like Bill Clinton (as I perceived him) as being forever sophomoric, in that he thinks talking about solving a problem is the same thing as actually solving it. The main thing is to come up with a p0roposal or program that seems feasible in a college dorm room bull session, and you've done your job. You've figured it out. No need to worry about follow-through -- that's for others to handle. You need to get on to thinking about the next big problem or trend or opportunity.
Well, maybe governing by inattention wasn't all bad. Both Clinton and Blair presided over periods of relative prosperity and solid economic growth. Economic trends tend to be more complex than most of us can even appreciate, let alone analyze, so presidents and prime ministers get both too much credit and too much blame for growth and recession; the roots are usually in a previous term, or in some discovery government never anticipated or encouraged. But chief executives who don't follow through on all their grandiose schemes sometimes meet the Hippocratic standard of doing no harm. Think how much better off the U.S. would be if Bush hadn't really cared about Iraq beyond a few posturing speeches.