Warfare & Tactics

Apples and pears. This goes for the entire drone line of both races, but most of all for these two ships. They have different roles, make decisions based on what you need/want from them.

Just standard PvP combat. Gangs of around 3-6 guys fighting wartargets in high/low sec.

The Amarr drone boat lineup has long been a sore point for Gallente pilots.

The actual performance difference between the races drone ships is very little IMO, you just have to realise the differences and decide what you prefer.
The Gallente drone ships are generally pretty straight forward in concept - Damage/tank. Drone + guns + tank in general.
The Amarr line up is more 'tactical' with ewar & cap warfare thrown in. - Drones + TD + neut etc.

Now a lot of people will say the vexor has been used in the same way the arbi has been for a long time. This is true and then question would then become why? If the vexor pilots have been copying the arbi setups doesn't that tell you something?

IMO they are very similar but with slight differences and tbh I'd train up Amarr dessy/cruiser/BC to 5 first then max out your drone skills then gallente dessy/cruiser/BC to 5 after that. This gives you the fastest progression to get good skills with a drone boat line up and while you are building up your skills in flying drone ship you cross train to gallente to access all the drone focussed ships.

I depends what you want to do with your drone boat.
If you want straight up DPS go Gallente. The Vexor brawls passably and has more drone bandwidth, which means more DPS, I used to love it. But then I discovered the wonder that is completely shutting down turret based ships with the TDs of the Arbitrator. You and your gang maintain range while your bonused disruptors hack 50 or 60 percent off your target's range. Plus the Arbi has a bigger drone bay. Not by much, but it means you can replace your spare flight of lights with mediums. A useful upgrade if you carry ECM drones, as light ECM drones are all but useless.

As for the Myrm vs Prophecy thing, do you ever fly with logi? The resist bonus of the prophecy is much more useful than the local rep bonus of the Myrm if you have logi.

Drones have issues, relying on them as your primary DPS source is bad move.

That being said gal ships are typically more effective for small gang/solo and such. Amarr are better fleet ships.

For small gang and solo, I'd go for Gallente droneboats over Amarr for sure.
That said, I'd still train and use Amarr droneboats, they're good. (just train those skills after the gallente ones).