Not exactly.
I’m asking if making your two attacks with shadow blade is more or less effective than dual wielding short swords, and making a booming blade attack, a regular attack, and a bonus action attack.
I’m thinking, at least without the elven accuracy feat, you might actually be better off not learning shadow blade, but I’m not a very good number cruncher.
Let's say 18 Dex for our example. A pair of ordinary shortswords could get 3 shots one boomong blade to get a (d6+4+d8) (+d6+4) +d6, for a total of 23 damage average, not including the average 9 damage from the rider if they move. At level 11 it is 27.5 for the attacks and 13.5 from the rider. With the fully developed 17th level cantrip it would become 32 average damage if all the attacks hit, +18 average damage from the potential rider.
Shadow Blade meanwhile (assuming your DM won't somehow let you boom with it) and a sidearm shortsword is( 2d8+4) + (2d8+4) + d6 for an average of 29.5 damage. Thus at either level 6 or 11 you are better off with a level 2 Shadow Blade if you think they won't move, and better off with booming blade on a shortsword if you think they will. At level 17 using real weapons with the cantrip pulls ahead. But, Shadow Blade can be upcast into a 3d8, 4d8, or 5d8 weapon. As a 3rd level, 3d8 spell, already very possible at level 6, dual wielding with a Shadow Blade is an average 38.5 damage, so better than a 6th level attack with booming blade even with the rider. Each upgrade of the Shadow Blade increases the average expected damage of the Shadow Blade by 9, which is the same amount that each upgrade of the Booming Blade increases it by if you get the rider, which is a pretty big if.
But let's put silly math theorycraft aside and look at practical gameplay. The game is full of magic weapons, some of which add damage riders, some of which increase your chance to hit. Meanwhile there is no such thing as a +1 casting of Shadow Blade. Against a high AC enemy you will often be better off using a magic weapon with a bonus to hit, even if theoretically the Shadow Blade would do more damage. On the other hand, if you are in dim light or darkness the Shadowblade gets automatic advantage and becomes almost always the best weapon you could use, other than a higher spell slot Shadowblade. With Elven accuracy it just becomes insane. Also it does psychic damage which is not widely resisted. The major drawback is less that it now precludes a booming blade attack and more that it precludes having some other concentration spell running and risks losing concentration itself.
But for gosh sake take Shadowblade. Just because you don't use a spell every encounter doesn't make it not worth taking, least of all for a wizard who learns plenty of spells. When it's moment comes it is incredible.
I would note that, I think serious dual wielding is mostly a mistake for Bladesingers after low levels. You need your first bonus action to start your bladesong, and if your using a Shadow Blade you need another round to get that going after (or possibly before). Subtract all the times you will use your bonus action to misty step, or cast cast some other spell, or control some other ongoing spell, and I think you are generally better off having a free hand for spellcasting and missing out on the occasional extra attack. By all means have a bandolier of disposible daggers for when the bonus action is free, but anticipate having better things to do with it.