They actually serve complementary purposes so running both makes sense, but you need to understand what each one does.
Malwarebytes Browser Guard focuses on blocking malicious sites, phishing pages, scam pages, and potentially unwanted programs. It's oriented toward security threats.
AdGuard is primarily an ad and tracker blocker. It filters advertising networks, analytics trackers, and can strip out intrusive elements from pages using cosmetic filtering (element hiding rules). It's much more comprehensive for cleaning up pages visually.
The reason one "takes over" from the other is probably because both are injecting content into pages and there can be ordering conflicts. What I'd suggest is: keep both, but in your browser extension settings prioritise AdGuard first, Malwarebytes second. They work at slightly different layers - AdGuard at the DNS/network request level and Malwarebytes more at the URL reputation level - so there's minimal real overlap.
If you still see issues with one overriding the other, disable the "in-browser" ad blocking in Malwarebytes specifically (it has a toggle for this), since Malwarebytes Browser Guard's main value is the phishing/malware blocking anyway, not the ad blocking.