I can PM you the mathematics underlying this assertion if you like Psapphy!
I'd actually rather publicly demonstrate some of the simple math you can go through, just for people to be able to see. Edge, avert your eyes!

The below scenario is favorable to the scimitar, in that the stats of the weapon are upper tier and the character is a strength-based character with a strength mod easy to achieve in that tier. It's realistically favorable, however. This plays down the longsword's base damage bonus significantly.
Weapon stats (both weapons): +5, +2d6, +11 from str mod
Scimitar: 26.5 avg
Longsword: 27.5 avg
In this scenario, the character has 4 attacks. They're attacking a critter they can hit on a 6 or higher (75%) on their first attack. They have improved critical and a keen blade. The numbers here represent the average damage of all crits + normal attacks over 20 rounds. Columns are 1st-4th attack, left number is regular attacks, right number is crits.
Scimitar:
218.625 + 357.75 = 576.375
145.75 + 238.5 = 384.25
99.375 + 66.25 = 165.625
25.175 + 2.65 = 27.85
20 round total = 1154.075
Longsword:
288.75 + 247.5 = 536.25
192.5 + 165 = 357.5
103.125 + 68.75 = 171.875
26.125 + 2.75 = 28.875
20 round total = 1094.5
Difference: ~5.3%
So as we can see, scimitar does have an advantage, but it's not absolutely world breaking. 5% is significant, but how significant?
Well, if there was such a thing as a d5, it's worth the longsword being 2d5 base damage. With the average damage from that being 105.45% of the 1d8 (27.5 vs 29), we're looking at 1154.15 -- pretty much identical to the scimitar.
However, 2d5 isn't a thing -- 1d10 is too weak, and 1d12 is too strong. These differences would amplify in the longsword's favor with lower tier weapons/characters. It likewise amplifies in the longsword's favor vs crit immune critters and critters with higher AC (the ones that, typically, you really NEED the better DPS against).
Speaking of crit immune critters, here's how the above works out with a crit immune monster over the same round/same AC/etc:
Longsword:
412.5
275
137.5
27.5
20 round total = 852.5
Scimitar:
397.5
265
132.5
26.5
20 round total = 821.5
Difference = ~3.7%
Now here's why I like adding a 2nd damage type to longsword over simply upping the damage to a purely hypothetical dice type. Let's say the longsword is multi-type and the critter we're facing has just 5/- slashing resist.
Take the 31 attacks that land over that 20 round period and subtract 5 from each and we're left with a 155 total subtraction. When you apply those numbers to the scimitar in the crit-vulnerable scenario, the longsword being able to bypass DR that comes out with about ~9.1% more damage. If you apply that 5/- to the crit-immune scenario, the longsword comes out with a whopping ~24.4% more damage.
Ultimately, at least in regards to this (I think somewhat realistic) set of scenarios in which a longsword is multi-type, the scimitar is worth about 5.3% more damage in ideal conditions for the scimitar (crit vulnerable, no DR), but the longsword is a more versatile tool. Now as I pointed out above, once you start throwing in things like massive crits, overwhelming crit, and particularly our old friend dev crit, the scimitar becomes rather nasty.
I think if you give longsword an extra damage type, the difference is ultimately relatively insignificant for most power levels on most characters with most gear in most scenarios on the server. I also think there's an argument for upping the longsword to 1d10 base along with the extra damage type given the scimitar's superior performance at high tiers, but that creates the problem of having to rebalance the damage values for most of the weapons in the game.
tl;dr, 3.0/3.5 really needed design people who could math.