Supply -> Battery -> Radio
Advantages: If there is noise on the DC supply, the battery could "filter" it a bit better than with a diode gate. Less voltage drop from the battery to the radio. If your radio is particular about supply - say, switches off at 11.9 volts or something - it might be better to connect directly to the battery. If your radio accepts a wider range of voltages, this is not as much of an issue.
Disadvantages: If the battery fails, the radio fails. You can't "hot-swap" batteries as easily.
Using a diode gate:
Advantages: If the battery fails, the power supply can run the radio and you can swap the battery without switching off the radio.
Disadvantages: A voltage drop over the diode gate; this can be compensated for by increasing power supply voltage, but you can't compensate for when supplying from the battery.
What I have is a simple diode gate float charger, with a resistor as a current limiter. This only float-charges the battery. If the battery has been worn down, it takes a while to get topped off again. (This design is similar to the PG40 - note the lack of "S" at the end, it's an earlier version with float-only charging.)
I use the float via a PG40S Wattgate to a 35Ah AGM battery.
While the PWRgate PG40 is float-only, the Super PWRgate PG40S contains a staged battery charger; that means KB1NXE is not simply floating the battery. After a power failure, when the battery is low, the PG40S will take the battery through the same bulk and absorption phases as a regular battery charger, before transitioning to the float charge once the battery has been fully charged. That means the PG40S charges the battery up faster than a PG40. That could be useful in a situation with intermittent power, say an emergency where you run your generator for a few minutes at a time, or where gird power comes and goes.
The 14.2 volt setting at the power supply is to compensate for the voltage drop over the float diode in the PG40S, however the manufacturer actually recommends setting the supply to 14.1 volts for gel and 14.5
volts for AGM as well as installing a jumper inside the PG40S. By doing this, the float charge will still be 13.5 volts, but the peak charging voltage will be raised to 14.2 volts since AGM batteries accept a bit more voltage in bulk and absorption than gel cells do.