Why the complete system matters
Both combine transmitter power, feed-system gain/loss, and antenna gain in the stated direction and polarization. They are not simply transmitter output.
The assumption that breaks it
Mixing dBd with dBi or adding gain before subtracting feed loss creates regulatory and link-budget errors.
Build or deploy it correctly
Choose one reference, convert consistently, use power at the antenna input, subtract real feed loss, add directional antenna gain, and state band, direction, and polarization.
Use the exact product guide, electrical topology, geometry, materials, loading, feed, return path, support, and environment. Mechanical fit or a visually similar arrangement does not establish electrical equivalence.