What other information I should be looking at?

Sensor size

The angle of view involves both the lens' focal length and the size of the sensor. A larger sensor will show a wider angle of view with the same focal length. A smaller sensor will show a narrower angle of view with the same focal length.

If images from two differently sized sensors are displayed/viewed at the same size, the image from the smaller sensor has been enlarged more to be viewed at the same display size as the image from the larger sensor.

Greater enlargement has disadvantages, too. Any blur in the image is magnified more. Any noise in the image is magnified more. The larger blur and noise are, the easier it is for our eyes to see them.

In the case of the Panasonic TZ80EB-S, the sensor is 1/2.3". The Canon PowerShot SX720 also has a 1/2.3" sensor, so that's not the difference in your case. The Canon, having the longer focal length, should be providing a more magnified view when both images are displayed at the same size.

Sensor resolution

The Panasonic has an 18.1MP sensor.
The Canon has 20.3MP sensor.

If one views both images at "100%" on a computer or tablet screen, the image with the higher number of megapixels will have a greater enlargement than the image with fewer megapixels. This is because viewing at "100%' isn't the same amount of enlargement for images with different numbers of pixels. "100%" means that each pixel in the image is displayed by one pixel group on the screen. If you're using a monitor with 96ppi pitch, then a 100% view of an 18.1MP 4:3 aspect ratio sensor will be like looking at a piece of a 51x38" enlargement. With the same monitor, a 100% view of a 20.3MP 4:3 sensor will be like looking at a 54x40.5" enlargement.

Again, the Canon has more pixels so should provide more magnification when viewing at "100%".

Based on the max length of both I was expecting Canon (with max length 172mm) is going to allow me to zoom in closer than Panasonic (with max length 129mm), but it's actually the opposite.

Why is that?

Digital trickery

The Canon camera includes a 4X digital zoom. Canon is pretty honest about it. Using 4X digital zoom and then viewing the results at the same display size as before using digital zoom would give you the same enlargement ratio as a 160X optical zoom would. In other words, you'd be seeing the same amount of enlargement as a 17.2-688mm lens on a 1/2.3" sensor. Or the same amount of enlargement as a 4.3-172mm lens on a sensor 1/4 as wide, 1/4 as high, and with 1/16 the area of a 1/2.3" (6.17 x 4.55mm) sensor.

Digital zoom is basically the same thing as cropping after the fact. The camera is only saving the central part of the photo and discarding the edges. Of course this reduces resolution, as only pixels in the central portion of the sensor are recorded. It also magnifies any blur and noise by the same amount. So for most of us, digital zoom doesn't really count because what is really happening is that the camera is just using less of the total area of the sensor to make things look bigger by blowing up the smaller image size to the same display size.

Panasonic includes what it calls "Extra Optical Zoom (EZ)", but in reality this is a form of digital zoom.

Notice that at the 42.5X setting the total resolution is reduced from 18.1MP to 9MP. That's to be expected if the sensor is linearly cropped by a factor of the square root of two (1.414). Guess what? 42.5 divided by 30 equals 1.417 (42/30 = 1.417). That's pretty close to the square root of two (1.414)!

Notice that at the 61.2X setting the total resolution is reduced from 18.1MP to 4.5MP. That's to be expected if the sensor is linearly cropped by a factor of 2. Guess what? 61.2 divided by 30 equals 2.04! Close enough.

Panasonic is Busted

Panasonic is trying to fool you into thinking you're getting optical zoom up to 60X when the lens used is only 30X longer at the telephoto end than at the wide angle end. They even include an additional setting for "digital zoom" to try and fool you. But notice that the 4X digital zoom can only be used at 2X when "Intelligent Zoom" is used?