What would be the best Soontir Fel Build?

Soontir Fel + PTL + RGT + Autothrusters + Stealth Device

or

Soontir Fel + PTL + RGT + Autothrusters + Targeting Computer

I run both builds. The targeting computer helps him deal more consistant damage, but the stealth device can make him impossible to kill. For me it really depends on if your list needs help dealing damage, if so go with targeting computer.

Shield upgrade. With all the vader crew out there it's worth it.

And with all the agility and autothrusters, the first damage in usually is a crit.

I like TC. Fel seems to often find himself defensively secure and I find myself wishing I could get more offense out of him.

I think it might be situational, since one is more defensive and one is more offensive in focus;

Soontir Fel + PTL + RGT + Autothrusters + Stealth Device

This would probably help you out when you're dealing with turrets, and might buy you an extra turn or two of fire.

Soontir Fel + PTL + RGT + Autothrusters + Targeting Computer

Assuming you're not going after a turret ship, this setup will let you arc-dodge yourself into a nice Range 1 unchallenged shot and pull off a good Target Lock+Focus combo for maximum damage.

So maybe it might help to know what you're running with Fel. If it was Vessery for example, you'd want the Targeting Computer build to make the most of Vessery's pilot ability.

Shield Upgrade helps you defy Vader.

Targeting Computer gives you excellent offense.

Stealth Device makes you incredibly difficult to hit (alongside Autothrusters).

There probably wouldn't be much argument about PtL and Autothrusters but if you're going to include that second modification I believe it will really depend on what you're facing and to a less extent what you are running with. As previously mentioned even the Shield Upgrade could be considered especially if you start looking at the chances that the first damage you take could be a [critical] result from any number of sources; if Fel draws the wrong face-up damage card things could become very difficult for him quickly.

The first build with auto thrusters and stealth device.

I prefer:

Soontir + RGP + PTL + AutoThrusters + Shield Upgrade

Just a bit of additional help against Vader, Feedback Arrays, and the occasional backstab by those fickle green dice!

Push the Limit, Autothrusters and Shield Upgrade.

Vader autocrit on Decimator, Mangler Cannon, soon to be Tie Advanced ATC... there is more and more way to garantee a crit and they can cripple the Baron. The Shiled Upgrade allows you to at least soak the first one. Autothrusters, arc dodging and the 2-3 defensive token should be enough to resist a lot of firepower (except for Vader in a Decimator, good thing you took a shiled upgrade!).

When I do triple Squints, Soontir gets the shield and AT, Jax gets Shield and Hull, and Turr gets VI and AT.

Targeting Computer just isn't worth it most of the time.
If you have that many points spent on such a fragile craft, you want your actions spent defensively.

PTL + Autothruster + Royal Guard + Hull/Shield is best, followed closely by + Stealth Device.

The first build with auto thrusters and stealth device.

i like that one too it's very hard to score a hit against him.

I think it is very hard to say which build is best as it is entirely dependent on what you are flying against. I think the answer lies in what you think you are most likely to encounter given your local meta.

Shield upgrade. With all the vader crew out there it's worth it.

And with all the agility and autothrusters, the first damage in usually is a crit.

This. And then some.

Shield for that unlucky green dice betrayal. And/or Vader auto-damaging.

PTL and autothruster... Whatever else you want with RGT is up to you and will likely work because, well, he's Soontir.