If you could nudge it £50 up there'd be this as an option:
Buy our AlphaSync Ryzen 5 8GB RAM 1TB HDD 240GB SSD RX 5600 XT Gaming Desktop PC from our wide range of Gaming Pcs
www.ebuyer.com
Which has a slightly faster CPU than either, a better graphics card than either, and faster RAM. Also the case will have better airflow. It would be the better investment long-term, I think.
Of the two above, it's annoying. The Acer has the better graphics card so would - mostly - perform better in today's games. However the PC Specialist model has an R5 3600 CPU, which would make it more futureproof with regards to future GPU additions. And the 1660 (the GPU in the PCS build) while not as fast as the 1660 ti, is no slouch for modern gaming. Also if your son took up streaming you'd have better performance and more meaningful CPU upgrade options on the PCS one because of the platform they chose to build it on.
Nothing else in PC world's catalogue is close to as good value at that price point as those two - so if you are buying from PC World, then it is definitely between those two.
Not sure which I'd pick. Maybe the PCS one.
Note that if you did decide to buy the Acer, you could actually buy the same thing from PC Specialist directly:
PCSpecialist is an award winning manufacturer of high quality computers and laptops, with reviews from many industry leading magazines and websites.
www.pcspecialist.co.uk
For £80 less - note the Sabre MK1 on that page. It's near enough the same spec as makes no difference.
If you don't mind buying refurbished there's this:
Buy Refurbished PC Specialist Tornado R5 Ryzen 5 3600 8GB 1TB & 128GB GTX 1660 Windows 10 Gaming Desktop from LaptopsDirect
www.laptopsdirect.co.uk
Which is like the PC Specialist on PC World but with a better GPU (same one as the Acer) and £50 less.
There are a few other refurbs on there too with decent specs.
Of all of those, I'd probably suggest the ebuyer alphasync if the extra £50 is doable and you're not locked to buying from PC World.