This is my current set up.
MacBook Air (11-inch, Early 2014)
1.4 GHz Intel Core i5
4 GB 1600 MHz DDR3
Intel HD Graphics 5000 1536 MB
+ OBS + Elgato Camlink (this is for game capture, Video AND Audio!!) + thunderbolt ethernet adapter + Line in Turtle Beach headset.
I run my retro consoles through an HDMI upscaler (this for my PS2, Dreamcast, n64 and Wii all first plugged into an RCA AV switch that is also a multi-tap for PS2), that then runs into an HDMI switch along with my retron 5. I send that into an HDMI 4 line in 1 line out, and have that plugged into the cam link and my TV at the same time. The camlink is super fast and I could easily play RPGs straight from obs, but probably not an FPS. I did a few streams running adobe illustrator in the background while using my Wacom tablet, and the computer still kept pace.
I will add that I don't currently use a camera as I have noticed it maybe starts to show some age when the Facetime Camera is running with a chroma key filter. The video audio quality is also
it streams well. No dropped frames. ran a VLC stream for 15 hours, no overheating, no problems. I stream a little more low rez than maybe most. The Gen 4 i5 is the minimum processor for the camlink by the way, so I guess either way you're looking better than me, and I do alright. Id goes with whichever one had more graphics memory, which may be the pro, no brainer. Though you mentioned this is just the streaming computer, so youll probably ok either way.
Computer wise, I love my MacBook air. The weight difference between a air and pro is noticeable, and the charge time for a air is like 30-45 mins. So if you're using your computer out and about as well, the Air is great.
If you need to also do some video editing, photoshop, or music creation, I would probably get a pro. Not as mobile, but more robust... and still plenty mobile. The extra muscle will get your further and there is probably more internal HD capacity on a Pro as well. My Air needs constant cleaning and dropping to my external, but I got a system going so its sort of second nature to keep up with it.
It's almost about time I get a new computer and I will probably get an Air, though I wish they still made the 11in model.