“Which is better, park domain names externally or on our own landing pages?”

I've mentioned useful external parking tools like Sedo and Parked. Both excellent services and can help you benefit from domain name parking.

However, if you have more than a 100 or so domains, then an external solution may not be right for you.
Why should someone else get all those metrics about what's performing or which keywords lead to which domain name, when you could get them for yourself? Parked domain names can help you better understand your customers.
You also can't direct traffic to domains parked in these services without violating their TOS. Nor will you know which campaigns are generating clicks like you can setting up the site like a property here.
If you want ease of use until you have traffic counts, then setup on Sedo or Parked. I've used both, found Parked was more flexible with better payouts, but controlling the domain in-house has much more long term value.
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Justin Hitt provides tools to industrial businesses to purchase domains at the best rates and secure your name on-line. For proven Internet marketing results, hire Justin's team at https://www.jwhco.com/