Interesting question. Let's look at the economy and economic decisions in the last 2 years of Clinton's adminstration:
Al Gore had been heavily involved in the Internet and this is when the Dot-Com bust occurs with flimsy internet-based firms losing billions and the world fiber optic network overbuilt to demand by 500% (Fortune) by 1999 so it'd turn into a political liability a smart opponent could make a lot of hay out of in the 2000 election while it was still unfolding and a very big deal (even to the media as it had allowed America Online to buy one of the largest media companies, TimeWarner for free as it's stock fell after the stock-paid acquisition embittering many TW journalists over their own 401k's and layoffs.)
This is also when the repeal of the Glass-Steagall banking regulations, the avoidance of regulating financial derivatives/securitization, and the commodities regulations were done, mostly under Phil Gramm, Robert Rubin, and some others. Clinton's grasp of economics (considerable) let him buy into the free markets arguments, what would have happened under Gore is hard to figure. Easy assumption is it would have happened anyway, but hard to tell. NOT having those extremely destructive choices slid through would have made this decade far less miserable, especially after 2007.
Gore was a big China fan too, remember the Chinese donations he accepted at the Buddhist Temple and that had been a significant factor in Clinton's campaigns (so expecting big bucks for a 2000 run would be logical) so China's unilateral access to U.S. markets, resources, technology (this is around the time of the Loral missile technology getting there and other defense technology transfer issues) so China would have a freer hand than they did while Wal-mart, their biggest U.S. customer, would lose a lot of clout that they'd had with their long-time friend and investment in the Clintons.
Gore doesn't make (well, be credited with making as "Waiting for Superman" tells us how much of the skill was the actual director/writer's work) "An Inconvenient Truth" or spend years trying to make a fortune from "Global Warming/Climate Change" campaigning, making that a far less significant movement with endless butterflies. If he's defeated in 2000, he probably still does as "Earth in the Balance" had been out for awhile by then and he needed something to do on the big stage.
While we're assuming Clinton dies flagrante delecto (like Nelson Rockefeller) or perhaps poisoned by Hillary (like Warren Harding probably was over his mistress) or has a stroke like Wilson or resigned after losing physical capacity to congestive heart failure like FDR should have (Thomas Fleming's book "The New Dealers' War" finds he was able to work only an hour or two a day during most of WWII), we're ignoring that Al Gore apparently had his own sex scandals in the wings given his divorce for long and multiple infidelities, assuming that blew up in 1998 instead of a decade later isn't much of a POD. Tipper had still ticked off much of the media and entertainment industry with her years of trying to clean up and further regulate their products so both donations and favorable coverage of Gore at this point would be far less likely and that would hurt a lot in the 2000 election.
Enron, Worldcom/MCI etc. are unraveling at this point and California's energy meltdown thanks to Enron's manipulations is just starting so running on the Clinton economy/economic policies going forward gets much tougher for 2000, especially depending on who the opponent was (McCain was pretty clueless about the economy, Gingrich or Lamar Alexander or Jeb Bush or Mitt Romney etc could have been very effective at this wedge.
Al Quaida's Sept. 11 attack really depends on who's President and how much of a priority they put into rebuilding human intelligence assets and making other big changes. Gore is unknown on that, I'm thinking he'd served on the Senate Intelligence Committee but could well be wrong. I suspect a President Gore would be far less likely to send in the Army or Marines than either Clinton or Bush II as Gore had seen combat firsthand as an Army reporter in Vietnam (Presidents who've seen friends die messily are always far more cautious about sending in the troops than the guys who do all their fighting inside the beltway.) So I'd suspect the Taliban would get much more of the Bosnian approach that Clinton used and Iraq would continue to get a "no fly zone", economic sanctions, and WMD inspectors as it had under Clinton.
I think we're mistaking the halo effect of dying while still iin office Presidents with JFK and FDR for a general effect (think about Harrison's, Lincoln's, Garfield's, McKinley's, Harding's VP's political capital from those deaths or how much the stature grew of VP's where the President was nearly killed/died (Ford/Rockefeller, Reagan/Bush, Truman (Puerto Rican nationalists shootout), FDR (Chicago Mayor died instead), TR (when shot making the speech)...) Dying of a heart attack in peacetime, much less from either during illicit sex or unhealth lifestyle, regardless of attempts to blame the Republicans or Gingrich for hounding him to death, just doesn't resonate (if you have Clinton get crushed by debris in the basement parking garage of the World Trade Center in the first Al Quaida attack, much different story.)
I think Hillary could just as readily turned away from politics after Bill's death, moved back to Chicago to a million dollar a year law partnership and resumed working on the child-defense causes that clearly spoke to her while raising Chelsea. Many more leave DC after a few intense years than stay forever.