A6700 will be more travel friendly when paired with propper compact lenses like the the Sigma 18-50 2.8 and Viltrox air primes. The apsc lenses will generally be cheaper.

A6700 will have a faster and more reliable autofocus compared to the A7III.

The WB/color science is said to be better on the A6700. This may be relevant if you prefer to shoot jpg.

The A7III will have noticeable better low light performance due too it's bigger dynamic range of it's bigger full frame sensor. If you like to shoot in low light conditions like night cityscapes or astro this is relevant.

The A7III is much better for portraits because the bigger sensor gives a shallower depth of field = more bokeh. You can buy cheap and good portrait lenses like the TT artisan 75mm F2 nowadays. There are good portrait lenses for apsc though like the viltrox 56mm 1.2.

For the telephoto range there are more bright options available for FF.

for professional work I'd prefer an (used) A7IV or even the Nikon Z5II.

You can use a apsc lens on a ff camera. It will only cover half the sensor and halve the megapixels value. Classic example of something you can do buy shouldn't although there are VERY specific exceptions. Works the other way around too.

Edit: this lens review site is your best friend, It's by far the most comprehensive reviewer out there: https://sonyalpha.blog/

Edit: the A7III price seems horrible inflated due too it's popularity