Just bought them both. What should I start play first? What are differences between them? Is it worth to play first games in both series or it would be better to dive right into second installments?

I haven't played Star Flight.

For Star Control, there's no need to play 1 before 2, although it wouldn't hurt to get some idea of the ships, perhaps. SC1 doesn't have a storyline as do 2 & 3, just a set of scenarios one can choose from.

I do still go back and play through the various SC1 scenarios for the fun of it, however! Indeed, I do this more often than I dust off SC2, because with SC1 you can play for a couple of hours, or more or less. SC2 is more of an undertaking.

While there's no need to play SC1 before 2, I would suggest it, if only because going from SC2 to SC1 will empnasize the age of SC1 in terms of graphics...

Hard to say - both Starflight games are excellent story/exploration games, but very, very dated in appearance and engine (i.e. clunky ui, very basic combat system). If you can get past that, play Starflight 1&2 in order (similar design, a continuing story, definitely worth playing both). Then play Star Control 2, which has almost identical game play to Starflight, but with much better graphics, interface and engine.

Star Control 1 is pretty much unrelated to 2 and can be skipped entirely - or just played as a separate strategy game with no real links to the sequel outside of the combat engine.

You didn't mention Star Control 3, but just in case - it feels like an attempt to combine SC1 strategy with SC2 RPG elements. Unfortunately it doesn't really compare with SC2 - not a bad game as such, just unlucky enough to be a sequel to a very good game.