Hosting you own data/integrating in your own CMS is of course possible with both, in Atproto that would be PDS.
But getting other peoples reactions in you own website is hard.
In ActivityPub there is a push model: If someone likes your post, they send a message to you AP inbox and you can use that message to bump an integer in your database.
Atproto in a way has a pull model: You need to read other users PDS. Of course you can do that, but only of PDS you already know. Unknown PDS of other unknown users stay unknown. ATProto solves this with Relays, which index PDS, transforming the data into a firehose. So if you want to get reactions, you'll need to run you own Relay or subscribe to someones elses Relays's firehose and do a lot of filtering.
In a way the Relay part of ATProto seem tailormade that only one or a few multi-million companies can run this expensive part of the network.
publish on your own site, syndicate elsewhere