They solve different problems, so neither wins outright: Bark reads content for risk signals and only pings you when something trips, while mSpy captures device-level activity - messages, call logs, location, app usage - and shows you the record. If the worry is bullying, self-harm or a predator in a DM, Bark's alert model fits better. If you want the SMS threads and call log from a phone you own and administer, Bark is the wrong tool and mSpy is closer.
Bark is content analysis. Connect the child's accounts or install its agent, and it scans messages, social apps, email and search for risk language, sending you an alert with a short excerpt rather than a firehose of every message. That is more humane for a teenager. The weakness is granularity: app coverage varies, and you cannot pull a complete timestamped call log out of it.
mSpy is device capture. On a well-provisioned Android device it shows SMS, call logs, keystrokes and location. Its iOS path is the usual one - it reads an iCloud backup, so the child must have backups enabled and you must hold the Apple ID. Pricing is regional and the renewal rate is the real rate, so compare the twelve-month total rather than the headline.
Disclosure: we build Ultimate Phone Spy - SMS, call log, location, web history and installed apps in one dashboard on Android 4.0+, Windows and Mac. Plans are $69.90/month, $40/month billed quarterly, or $16/month annually (pricing). We do not cover iPhone at all; that is on the system requirements page.
Try the free tiers first. Apple Screen Time with Family Sharing gives app limits, downtime, Communication Limits and location. Google Family Link does location, app approval and screen time on Android. Both run through the account holder's credentials, so a child cannot quietly switch them off.
Decide on the requirement, not the vendor: warnings about dangerous conversations points to an alerting product; the underlying record on a device you administer points to a capture product. On an iPhone no vendor can give you live iMessage content - Apple does not permit it, whatever the ads say.