I've been experimenting with a number of builds with my gaming group but I was wondering and figured here (and bgg) are the best places to ask.

If you have 1 ship and unlimited points for upgrades what would be the hardest ship to take down? Both for rebel and empire. Not concerned with hitting other ships at all just who can survive the longest.

And with those Same rules what would be the heaviest hitter, as in what single ship build has the highest potential damage in one attack?

Assuming that you're being a standing target...

The hardest ship to take down, for the Empire, is gonna be a Firespray, hands-down, preferably with a Recon Specialist and Push the Limit.

Vader in the Tie Advanced is probably 2nd on their side, though that's pushing it with a fully defensive Shuttle.

The hardest ship to take down for Johnny Reb is DEFINITELY a named YT-1300 with the Chewbacca crew, the Millennium Falcon title, and Push the Limit.
The 2nd hardest ship to take down for Johnny Reb is Luke Skywalker's X-Wing with an R2-Astromech, a Shield Upgrade, and a defensive Elite Pilot Talent of your choice.

Yeah, here's the best I can come up with:

Chewbacca (42)
Push the Limit (3)
Flight Instructor (4)
Recon Specialist (3)
Shield Upgrade (4)
Millennium Falcon (1)

Or

Boba Fett (39)
Elusiveness (2)
Flight Instructor (4)
Shield Upgrade (4)

Or maybe:

Captain Yorr (24)
Sensor Jammer (4)
Flight Instructor (4)
Recon Specialist (3)
Shield Upgrade (4)

For your original question it would probably be chewie falcon + mf title + luke gunner + recon specialist + hull upgrade + PTL + cluster missiles. That gives you 14 hit points, can't take crits, can use ptl to get two focus and a evade each turn for added defense.

For imperial it would probably be boba fett firespray + slave 1 title + recon specialist + shield upgrade + PTL + HLC + proton bomb + assault missiles + advanced proton torpedoes.

One ship with no regards to cost....

This isn't the other party in the Y-Wing vs. TIE Interceptor thread we've seen where someone believes all battles should have equal number of ships on either side but not bothering to check the points on each side would it? Sorry for asking but a recent post has covered how crazy comparing ships is if cost is NOT a consideration.

For the Empire some version of the Firespray (Boba's dial changing combined with Navigator is the most defensive) or Vader w/Engine Upgrade are where it is at. For the Rebels a named Falcon is definitely the hard although when it comes to fighters I'm torn between Luke and Tycho.

Edit: I just occurred to me (and I finally got back to a keyboard) that the hardest Rebel ship to take down in any kind of one on one situation may be:

Ten Numb + Advanced Sensors + Engine Upgrade + Push the Limits + offensive upgrades.

Reason: High PS means most other ships should have had to move first and then the combination of Advanced Sensors, PtL, and Engine Upgrade along with the B-Wing's Barrel Roll should allow it to get somewhere an opposing ship can't even shoot at it. So many possible end points and often a number of different ways to get to them if rocks or other things are in the way.

Luke Skywalker

Expert Handling

Shield Upgrade

R2D2

imho a skilled pilot could outlast even the big base ships. barrel roll out of trouble, shrug off target locks, green move and recharge a shield every 2nd-3rd turn, keep out of the close combat (thats more for heavily armoured falcons, slave1's and shuttles) and cross ur fingers u can roll focuses on defense to get Lukes free evade

I guess on the Falcon build it depends how many enemies you are facing. Against multiple enemies you want high hit points and lots of evade dice. Against a single ship you want manuverability to stay out of firing arcs.