Upvote:-2
If you have 25 minutes between arrival and departure, not boarding, you would have to be very lucky to catch that connection. Many airlines close the gate 30 minutes before departure. You usually have a few extra minutes while they "last call for ..." you, or not, depending on how tight the schedule to their departure slot is.
VIE isn't big, but it does have two terminals and three gate sections - labeled C, D and F/G on this airport map. If both your flights are at the same gate, and you are one of the first off the plane and you are at the gate and not having a bus transfer and your incoming flight touched down on time or even early, you may make it before they close the gate of your departing flight. But only then.
I wouldn't book such a connection, unless the airline will manage your transfer and guarantees you will make the connection or if not they will put you on the next available plane free of charge. I mean, if they pick you up at the incoming plane with a car and drive you to the departing plane - then yes. Otherwise, no.
Note: I'm not entirely sure if you need to go through outgoing passport controls in your scenario, though the few times I've done so in VIE they didn't take more than a minute or two.
Upvote:2
I had a 40 minute Schengen to non-Schengen connection in Vienna late at night last December. Incoming flight was 5-10 minutes late, we rushed a bit but had time to spare (boarding hadn't started when we reached the departure gate) so it doesn't seem completely unrealistic. Don't remember waiting much for the border check, even with a non-EU passport.
Regarding EU261, I don't find the regulation very clear but the EU Commission suggests you should be covered, at least if the incoming flight is delayed. Quoting the website:
You are not entitled to compensation if you miss your connecting flight due to delays at security checks or if you did not respect the boarding time of your flight at the airport of transfer.
Flights within the EU or departing from the EU are covered in any case, the only question is who would be responsible for handling your claim.