You should definitely use LUKS2 whenever possible. It is the newer header format and overcomes the limits of the (legacy) LUKS1 header. It is the default since cryptsetup version 2.1, but this alone doesn't say much. The Password-Based Key Derivation Function (PBKDF) is the big change.
If you use the PBKDF2 algorithm it doesn't really matter if you have a LUKS1 or LUKS2 header (even though LUKS2 is more resilient, as it has a backup copy of critical data). The newer Argon2i or Argon2id algorithms introduced with cryptsetup version 2.0 use up more space, which is why Argon2 doesn't fit into the smaller LUKS1 header.
Also, Argon2, as it is a newer algorithm, is probably even safer than PBKDF2, but it comes at the cost of more memory (RAM) consuption as well as requiring the LUKS2 header.
From the cryptsetup.8 manpage:
For PBKDF2, only time cost (number of iterations) applies. For Argon2i/id, there is also memory cost (memory required during the process of key derivation) and parallel cost (number of threads that run in parallel during the key derivation).
Since cryptsetup 2.1 defaults to the bigger LUKS2 header, it also seems to default to Argon2i instead of PBKDF2. I recently manually created a LUKS partition on my Debian Linux, current stable 10.4 (as of this writing; might have been 10.2 or 10.3 when I created the LUKS partition), and it was set to LUKS2 with Argon2i.
The problem is that GRUB2 doesn't support LUKS2 on most distributions (as of this writing), so a default installation will (have to) default to LUKS1 anyway, at least if /boot is affected, otherwise it cannot boot. There is this guide on how to do this properly on Debian 10 "Buster". Ubuntu is originally based on Debian, so it may be similar. The trick is to have a separate LUKS partition with a /boot partition on its own, and to convert this partition back to LUKS1 for GRUB2 to find the Linux kernel and initramfs. Alternatively the root partition, if it holds /boot and is LUKS2, may be converted back to LUKS1 in its entirety. In both cases it is a good idea to add a keyfile for one additional LUKS keyslot and to copy this keyfile into the initramfs (or configure the initramfs to find the keyfile). GRUB2 will ask for a passwort for /boot, but when booting the kernel and the initramfs, a password would have to be entered again - which is the same password for the same partition, if /boot is on the root partition (or another password for /, if it is different from the /boot partition). This can be avoided if the initramfs uses a keyfile, which is safely stored on the encrypted /boot anyway.
Also noteworthy: In January 2020 GRUB2 got a patch and is now able to handle LUKS2 headers, but only with the legacy PBKDF2 algorithm. There are two problems here. The first is that it takes time until such a patch comes into a release version and even more time until it is distributed. Debain 10.4 (stable-branch) for example has still an older version of GRUB2 which is unable to handle LUKS2. And second, Argon2 is not supported by GRUB2 even with the mentioned initial LUKS2-patch.
If you were to create a LUKS2 /boot partition, chances are high that it will default to Argon2i. For /boot you would have to specify
--pbkdf pbkdf2 while creating a new keyslot for GRUB2 (with the LUKS2-patch) to make this work.
cryptsetup luksAddKey --pbkdf pbkdf2 /dev/<device>
I highly recommend reading the Arch Wiki pages for further information on how to work with cryptsetup and LUKS volumes.