You should have no issues running those add-ons in parallel. However, you should be considering how your users are using the products if both add-ons are updating JIRA issues.
As for everything, test it on your staging/dev instance and if you notice any issues please raise a support ticket with Atlassian and Big Picture.
I second what Bhushan Wrote. Two plugins should not interfere with each other though, please make sure not to make updates to the same Jira issues whenever both apps are active in separate tabs. This could cause issue.
Whenever you require any additional help with BigPicture, you may contact us directly by sending an e-mail to firstname.lastname@example.org.
Piotr of SoftwarePlant
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