Where are you based? In the UK?
Xiaomi brands are generally not sold in the US.
They are both Chinese brands, but Xiaomi (with their Poco, Redmi and Xiaomi models) are
infinitely larger (top 3 Worldwide alongside Samsung and Apple iirc) and much better specified for the money, now have very good long term support, though updates can be slow to arrive.
The software controls and useful options are up there with Samsung or Google (without AI intelligence). You would not suspect they are a Chinese brand, as you would that Samsung are from S. Korea.
Any old complaints about too many added apps (Samsung are worse) , adverts and shutting down of running apps can be rectified in Settings.
It depends how important a ruggedised phone is to you, but you will sacrifice poor hardware like the old, budget processor and screen type. I haven't looked at the second model Doogee you mentioned.
If you are hitting the £300 - 350 mark, there are Xiaomi several I can recommend. You would be well advised to budget about £15 - 20 for a case and around £9 for a pair of Tempered Glass screen protectors (1 spare). Ibywind on Amazon are very good screen protectors. Spigen among others make several different cases for most all models. Both items should see you covered.
I have my Xiaomi Poco F2 for 3.5 years. The other member mentioned had changed to the Redmi Note 13 Pro Plus a few months ago.
Reviewers rate the model you mentioned as the value / soecs choice of the 4 Note 11models.
The top Xiaomi 13T and 13T Pro can be found under £440 at CEX as new.
Samsung have good models in the 2022 S21FE, and A34 A54 models now being replaced.
Doogee have been an odd choice for the very few. I don't think the S98 has updated to Android 13 and 14 yet, and you may have to install a ROM to update
Nokia brought out a rugged phone last year, the XR21. A good brand in the past, but again LCD screen type (for better shock resistance over OLED probably) , Victus screen glass prone to scratches but otherwise OK, and disappointing though competent processor.
Xiaomi phones have Infrared ports on I think all models.
Try to download the Mi Store app where you are, or check their website. I've seen amazing one day or weekly reductions, plus coupon and points discounts.
(I gotta stop re - editing. Doc!)