To look at this, we need some basic statistics, particular the "standard deviation." This is a figure which measures how much variation exists in a set of data. A low standard deviation indicates that the data points tend to be very close to the mean; high standard deviation indicates that the data points are spread out over a large range of values. For instance, two sets of data 1, 7, 1, 7 and 4, 4, 4, 4 have the same mean, of four. But the first set will have a much bigger standard deviation. That would be what you're looking for in a "boom and bust" team: big swings in the number of wins over the year. I've used the data for all major-league teams from 1998 through 2012.
As another stat that might gives us some insight, I also worked out the average difference in wins from one year to the next. For example, the 1999 D-backs won 100 games: that counts as 35, because it was that many more than the 1998 D-backs. The 2000 D-backs won 85, so that counts as 15 - we're not concerned about more or less, it's just the magnitude, not the direction. Do this for all the seasons from 1999-2012, and you can get a number which is the average change, year to year. A big number would also indicate a volatile franchise. Here are the results, sorted by standard deviation, along with the average, high and low numbers of wins for each team.
This does seem to show some evidence supporting the "boom or bust" claim. Our standard deviation is fourth-highest, and our average difference in wins is third-highest, at almost 17 per year. This is heavily due to the 1999 and 2011 seasons, when we went worst-to-first, with the two biggest improvements by any National League teams in our era, and the 2004 team, who were 33 games worse than their predecessor. However, the leader in both categories are Seattle: so they are clearly boomier and...ah, bustier than Arizona.
Some other stuff to note. You can get a fairly good idea of boom/bustiness by simply looking at the gap between a team's best season and their worst. The Mariners score a 55 there, we're second at 49, and the top five in standard deviation all have a gap bigger than forty. But it's important to note that stability does not necessarily equal success. Down at the bottom, we find the Blue Jays, who have been between 67 and 88 wins for seventeen consecutive seasons, and the Pirates. Neither franchise have seen post-season action since before thewere a gleam in Jerry Colangelo's eye.
But above them, are the Dodgers and Yankees, who have both been fairly successful. That's putting it mildly in the latter's case: New York has averaged close to six wins more per season than the second-best team, Atlanta, since 1998. There's also some evidence of decent competitive balance, with 90% of the league - everyone bar the Blue Jays, Pirates and Royals - having had a 90-win season, and all bar four (the A's, Cardinals, Red Sox and Yankees being the exceptions there) having had a 90-loss season over the past 15 years. 23 teams have had both. So I don't think it's possible to mitigate those "peaks and valleys" mentioned by Towers entirely.
Obviously, Towers isn't aiming for a team that will go .500 every year. He wants to raise the floor, so we don't get those seasons with 90+ losses, because coming back from there is not easy - 2011 was very much the exception, not the rule. If the floor projection of the team becomes somewhere in the high-70's, there is probably a greater chance of competing in any given year. That's especially given the additional wild-card now in play, which may mean that 88-89 wins is enough to reach the post-season in most years. You certainly can afford to be a bit less "peaky," and still make the playoffs.