The C will put out more firepower over all due to better heat management.

No.

Prime: 2 erll, 2LRM20 + run = 38, drop 34. Then either 1 erLL gets dropped to be heat neutral, or 1 LRM20 gets dropped to reduce heat by 2 for 2 turns:

20 + 24 damage, followed by 34 damage, alternating. 39 average.

The C: 2 erLL + 2 LRM15 + uAC5 at double + AMS + run = 39 heat, so 9 over. Pretty undesirable in my book to take those penalties when your enemy doesn't have to.

But 24 + 18 + 7 damage for the uAC5 on average = 49. Then 3 turns of running 39 damage while you cool down. Across 4 turns, it's 41.5 average, but 1 turn with a move and a to-hit penalty. Not sure that's a wash for just 3 extra damage, average.

Dropping the erLL allows you to push 39 damage each turn without ever having heat issues, so the same as a Prime.

Once you're close, the damage potential for the Prime is 1 erLL, 2 erML, 1 MPL, 1 LRM20: 43 damage for 34 heat.

The B can go to 1 erLL, 1 erML, 2 LRM15s, 1 uAC5: 42 damage for 31 heat.

The C will shoot down some of the Primes ranged fire w/ AMS.

Giving it a slight edge, yes. It's just AMS.

But the Prime's ammo doesn't last long anyway, so at some point the math is energy only.

Prime Better? Maybe. Lots Better? No.

We agree.

As a star mate I'd take the C for sure since lower BV will allow me to get an edge with one of my other mechs.

That's a meta argument. Then universe doesn't deploy stuff with BV.