You don't see many fake movements in gold cases, I'd wager that they're authentic. Both nice watches of different styles. I don't usually like quartz watches, but I like the style of that Omega. Probably just needs a battery. The Longines is a nice, quality, hand wound movement. But I don't care for the style myself. Up to you. Nice couple of watches.
'07 Single Ring Old Type, '21-'29 Gold Old Type Ball End Handle, '28 New Standard Gold, Gold NEW Ball End Handle(long teeth), Gold NEW Common Bar Handle(short teeth), NDC Gold Tech(3), '59(E2) Red Tip
GEM Micromatic Open Comb Antenna Handle, Schick G1(2), Schick G8, Rolls Razor Imperial No.2(5), Rolls Razor Viscount(3)
A. White CopperHead 6/8, D. Peres 5/8, Hamburg No. 49 6/8, Wade & Butcher 6/8, German Cutlery Co. 5/8, Wosty Pipe 5/8 wedge