The Federation’s characteristic bonus is to hull integrity.
The Tribe’s characteristic bonus is a lot to hull integrity.
Does the Federation still have an advantageous niche? What do they do better than other races in the current field?
imho, all the races need to be rebalanced. although the rebels still put up a good fight against the tribe
the tribe have severe armor and shield penalties. the federation doesn’t. 
The Rebellion is my race of choice. I’ve seen the Alliance put to good use. Not the Empire or Order much, admittedly…
Obviously, but how do you leverage that into a play advantage that isn’t better implemented as some other race?
There are now 6 other options. What would make you choose the Federation? Other than the pretty blue hulls.
missions where shields and armor are critical to winning, but hull integrity is also something important. The Federation has the most advantages, yet they’re less emphasized than the other races’ abilities.
It’s not always about the racial. Swarm’s global +15% to speed is higher than anything the Rebels can match.
Feds have:
Small 8 hardpoint cruiser.
Racial specific Fusion Beam can penetrate non-reflective shields with a higher base tracking than default heavy beams.
Small, effective frigates.
Medium tier airforce.
Feds were decidedly second-place runners (behind rebels) when it was just the stock races. The fed fusion beam is THE reason to use reflective shields.
Feds don’t have anything hilariously overpowered like the tribe racial, but they’ll always be a solid race with existing mechanics, despite never really having the ‘best’ of anything.
This sums up why my most effective ships are all Federation. I favor a “balanced” style of play, and the Feds are the only one with racial bonuses that don’t consist of one bonus off the top of the charts and everything else varying from ho-hum bonuses to borderline crippling penalties.
I think the Feds are the strongest. Flexibility has real value in and of itself and the Federation Fusion Beam is the best weapon in the game. I try other races from time to time, but I have always gone back to the Feds. Take a look at the SAC challenges for example. It’s not a coincidence that the most common race is the Federation.