Tasha's Cauldron of Everything updated Bladesinger wizards (originally from Sword Coast Adventurer's Guide) in a few key ways. For one, it expanded the Extra Attack feature to allow casting a cantrip in place of one of your attacks. I really like this addition and think it's great for character concepts that seamlessly blend spellcasting and swordplay.
It also, however, changed the Bladesong feature from "twice per short or long rest" to "proficiency bonus times per long rest." Most players these days don't seem to really use short rests, so this is probably meant to be an improvement, or at least a simplification to reduce bookkeeping. But I think short rests are a fun and important mechanic. The new version of this feature makes me feel like I need to study up in the school of divination just to decide when in the adventuring day to activate my bladesong!
Here's the thing: the introduction to Tasha's Cauldron of Everything says "Everything in this book is optional." Does this mean you can take individual parts of the TCE Bladesinger, but otherwise use the SCAG Bladesinger? That is, can you create a Bladesinger that regains their two uses of bladesong after a short rest, and can also swing a scimitar and shoot a fire bolt as part of the same Attack action?
I know TCE is a big stack of of "this is up to your DM," but it is allowed in Adventurer's League, so I still think it's fair to consider what's "rules as written" according to Tasha's.
This question can probably also apply to other things that were introduced in one book, then re-introduced "optionally" in another book, like the Artificer (which, ignoring Unearthed Arcana, was originally printed in an Eberron book, then was also expanded in TCE)
Best Answer
The most recent printing or publication replaces earlier ones
In general, if there are multiple versions of the same thing, like a race or class description, the latest publication prevails.
For example, the hobgoblin race in Mordenkainen Presents replaces the earlier one from Volo's Guide to Monsters. Likewise, the Tasha's version of the Bladesinger class replaces the earlier one from Sword Coast Adventurer's Guide.
Wizards announces this on a D&D Beyond page about legacy content:
Likewise, the Adventurer's League Players Guide advises on the first page under "What Rulebooks should I use?"
The "books listed below" include both Sword Coast Adventurer's Guide (SCAG) and Tasha's Cauldron of Everything. So, you cannot cherry-pick and combine the best from different iterations of a class to min-max something stronger. You are supposed to use the latest version of the class, exclusively. In this case, Tasha's, as it was printed later than SCAG.
As @Someone_Evil points out, in this specific case the SCAG also received errata, so that its Bladesong feature now uses the same rule for how often you can use Bladesong as Tasha's:
(What you negotiate with your DM as homebrew house rules is an entirely other matter, of course).