Taproot was successfully blocked, and will be operational by mid-November, as block 709,632 was confirmed on the Bitcoin network. The arrival of this improvement brings with it the use of a new address format, the SegWit v1, that could mean a reduction in network fee payment, but is it really so?
The Bitcoin portal Optech, in its newsletter #155 published last June 30, makes a brief analysis on the comparison between transactions with P2WPKH (SegWit v0) and P2TR transactions (Taproot/SegWit v1).
The premise for differentiating both types of transactions raises the following question: will Taproot transactions be cheaper than those using SegWit v0? To this end, the Optech team compares the single-signature transactions, recording 2 inputs and 2 outputs. To do this, they used the transaction size calculator, the portal’s own.

How a Bitcoin transaction of 2 inputs and 2 outputs is composed.
To understand a little better how this comparative table works, it is necessary to be clear what the transactions (TX) of 2 inputs and 2 outputs are about. Let’s take as an example that a user wants to send a TX of 1 BTC, in which he has the balance distributed in different addresses of his wallet: 0.6 BTC in one and 0.6 in another. The total sum of the balances is 1.2 BTC.
Now, since the balance of your wallets is higher than the amount to be sent, there must be a 0.2 BTC withdrawal or return. However, due to the very nature of Bitcoin transactions, UTXOs must be spent in full, and the remaining must be returned to an address in the portfolio itself, which generates a new UTXO.
We see then that in this example there are 2 inputs, which would be the balances of 0.6 BTC in each direction; and the two outputs, one of 1 BTC and the withdrawal of 0.2 BTC.
Something to highlight is that, the greater the inputs or outputs, the greater the weight of the transaction.

Differences between SegWit v0 and Taproot transactions
According to Bitcoin Optech’s comparison chart, Taproot transactions would be slightly heavier than SegWit v0. It seems counterproductive, but the weight difference is from 208.5 bytes to 211.5 bytes, a difference just over 1%.
However, within the newsletter it is mentioned that, while Taproot transactions seem heavier, and therefore more expensive, “a closer look” it is revealed that there are more advantages to using P2TR or Taproot in single-signature transactions, in which a single user signs the exit operation. In contrast, multisig transactions, of 2 or more, are usually heavier.
One of the main advantages is that it will be cheaper. In P2TR addresses (Taproot) transactions could cost up to 15% less due to a feature when choosing the addresses to spend from. In native SegWit addresses, the actual size, according to the previous example, it would reach 235.5 bytes, while in Taproot it would remain above 211.5.
It is also possible to predict a more accurate commission rate. With ECDSA signatures, used in legacy and SegWit addresses, the actual size of the transaction could not be known until the subsequent creation of the transaction. With the new Schnorr firms, which will also use Taproot, the actual size is known in advance, allowing better calculation of the commission to be paid.
In addition to this, according to the Bitcoin Optech portal, Taproot also features privacy enhancements and hardware resource savings.