Having used both extensively, they are both very fine and capable products. Besides the 2019 MacBook Air 8/256 and 2019 MacBook Pro 8/256 (1.4 GHz), I use well-equipped 2017 iMac Pro and 2018 Mac mini desktops. As a pro iOS developer using this stuff 12 x 7, having access to a fine-grained assortment of tools is nice.
Comparing the MBA and MBP with same RAM (8GB) and SSD (256GB), you can start the comparison on even footing, and then consider the advantages of each that are more important to you.
While the MBA is only slightly lighter on paper, it's geometry (slanted design and gradual tapering) make it feel a little more compact and ergonomic. It has unique character you can get used to and appreciate (like a favorite camera). It will handle practically anything you throw at it. I like that it can use the same charger as my 12.9 iPad Pro, helping with traveling light.
The MBP (1.4GHz) is amazingly fast for only a moderate increase in cost over the MBA. The 2 extra cores make a considerable difference in performance not only for intense tasks, but there's also a noticeable improvement to just about all user interactions and animations. The higher performing graphics is something to appreciate at times when it matters.
So both are great machines, each emphasizing something a little better then the other. MBA for size and MBP for performance. For your use case for business apps both are well suited, with the MBP experience being a little snappier and the MBA being a little more portable. For video editing and photo editing, the increased performance MBP will really shine here. The MBA will get the job done too, but you'll have more time for coffee while rendering your clips.