Is containerized deployment of jenkins on ECS better than running jenkins inside EC2 instance to secure pipeline information?
Running Jenkins on EC2 is the better option. It's better to keep the functions that manage your containers separate from the containers themselves. I know this is different than Kubernetes, but this isn't Kubernetes. 

Build an ELK Stack on EC2 as well and send your build logs to that instance so you can go through them when troubleshooting. It sounds like your setup is good with data volumes and such. I would recommend that you use Fargate instead of EC2 nodes for your workers though. Not clear which you are using. 

There are simpler solutions than Jenkins as well. You may want to consider CircleCI, GitLab Runner, TeamCity, Bamboo, and others. Jenkins is made to do all things and is a good place to learn the process, but if an alternative does the job just as well and more easily, then try that. My current favorite is GitLab Runner. It's just simpler and it integrates your Git repo with the CI tool in addition to having its own image repo for you to use (in certain versions). 

You can also give EKS a shot. I haven't tried it but Kubernetes is a superior product. It's far more complex, but definitely a better orchestration tool.