Verdict
Start with network tracking while you still need to recruit publishers. Move to own software only once the programme is mature and most partners already know you.
Cost and ownership
Own software costs a fixed licence and your implementation time, but no override on commissions. At high volume that is significantly cheaper.
Partner data and relationships also stay with you instead of with the network.
Reach and recruitment
Networks have a marketplace where thousands of publishers actively look for programmes. You lose that inbound flow entirely with own software.
Without a network you approach, contract and pay every partner yourself, in every market and language.
Measurement reliability
Server-side tracking and first-party cookies are possible either way, but networks handle maintenance for you with every browser change.
With own software you own tracking-loss monitoring and fraud control.
The practical path
Many brands run both: a network in new markets for recruitment and own software for core partners they already know.
Make sure you exclude double attribution, or you pay twice for the same sale.