do I need the 15.7.1 update or should I upgrade to 16?

At this time, you can choose between updating your iPad currently running iPadOS15.x to iPadOS 15.7.1 (with essential security updates) - or you can upgrade to the next major version, this being iPadOS16.1.1.

iPadOS16 has many new features and capabilities.

Due to essential security updates, you should choose one or the other. Whether of not you are ready to jump to iPadOS16 and its many advanced features and benefits, only you can decide.

Information about the new features of iPadOS16 can be found here:

iPadOS 16 - Apple

Just my own opinion here, but I feel iOS/iPadOS 16 needs a few more point updates before I would even consider upgrading all of my familiy's compatible devices.

I think iPadOS 16.1 still has some quirks and bugs in it that, I feel, need, maybe, a point 3 or point 4 update, so Apple can address these various, sundry issues, with iOS/iPadOS 16.

There appears to be some nagging battery draining issues, with no real solid solution/s.

For another example, HDMI video adapter support issues.

Still some issues with the Home screen/s and finger getstures.

Some “new to iPadOS 16”, external drive support issues, too!

I'd like to see Lock screen customisation come to iPad and iPadOS 16, as well, but that feature may, or may not come to iPadOS 16.

For now, I elected to just update my 2015/2016, 12.9 inch screen iPad Pro to iPadOS 15.7.1.

My iPad is too old for ANY of the newest and coolest features of iPadOS 16, so my iPad Pro model will only get the basic features set of iPadOS 16, anyways.

So, I am in no real hurry to upgrade.

I'm waiting for iPadOS 16 to become more stable and reliable.

That will take a few more point updates from Apple to address and straighten out some of the current “kinks” with iPadOS 16.

In the end, the choice is yours.

Like always, iOS/iPadOS upgrades/updates are one way/direction. Up/Upwards.

Best of Luck to You!