Based on the comments, the airline you were booked to travel with is Wizz Air, which is an EU based airline so EU261 rules do apply.
Whether the airline likes to style this as a cancellation and rebooking, or as a delay to the original flight, it does not matter - both result in the same level of compensation, being 250 Euros. For a cancellation, you were not notified more than 14 days prior, and for a delay you definitely arrived at your destination more than 3 hours late - either of these criteria result in EU261 compensation rules bring triggered.
If you were informed of the cancellation less than 14 days prior to the scheduled departure date, you have a right to compensation. The airline has the obligation to prove if and when you were personally informed that the flight was cancelled. If this is not the case you can contact your national authority for further assistance.
EU261 air passenger rights guidance on cancellations.
If you arrived at your final destination with a delay of more than 3 hours, you are entitled to compensation, unless the delay was due to extraordinary circumstances. The airline has to prove this by providing, for example, extracts from logbooks or incident reports. The air carrier should give this evidence to the relevant national enforcement body as well as to the passengers concerned in line with national provisions on access to documents.
EU261 air passenger rights guidance on delays.
The issue here is collecting it - airlines are bleeding cash right now and very few are handing over EU261 compensation. There may be a legal claim to be had, but unless the airline rolls over for you, its going to be a hard slog. You can complain to a relevant aviation body in either Wizz Airs home country, the origin airports country ir the destination airports country and see where that gets you, or you can take legal action yourself.
Wizz Air is definitely in the wrong here with regard to denying compensation - EU261 rules are all about preventing airlines from doing precisely what Wizz Air are attempting to do in your question...