Article 5 or EU regulation 261/2004 reads (my emphasis):
- In case of cancellation of a flight, the passengers concerned shall:
(a) be offered assistance by the operating air carrier in accordance with Article 8; and
(b) be offered assistance by the operating air carrier in accordance with Article 9(1)(a) and 9(2), as well as, in event of re-routing when the reasonably expected time of departure of the new flight is at least the day after the departure as it was planned for the cancelled flight, the assistance specified in Article 9(1)(b) and 9(1)(c); and
(c) have the right to compensation by the operating air carrier in accordance with Article 7, unless:
Article 8 is the bit of the regulation that, among other things, entitles you to a refund within 7 days if your flight was cancelled and you choose not to ask the airline for a rerouting. Article 5 clearly implies that you should get that and the compensation (at least if the conditions to deny compensation do not apply and in particular if the cancellation is not due to “extraordinary circumstances” beyond the control of the airline, which includes strikes and air traffic control decisions).
Where things get a bit hairy is that the notion you should get compensation for a three-hour delay is nowhere to be found in the regulation. Originally, it only covered cancelled flights, which would make your question moot.
The reason why the EU website says otherwise is that this has been extended to flights delayed for more than three hours by case law (and in particular case C‑402/07 and C‑432/07). The decision itself is as follows:
Articles 2(l), 5 and 6 of Regulation (EC) No 261/2004 of the European Parliament and of the Council of 11 February 2004 establishing common rules on compensation and assistance to passengers in the event of denied boarding and of cancellation or long delay of flights, and repealing Regulation (EEC) No 295/91, must be interpreted as meaning that a flight which is delayed, irrespective of the duration of the delay, even if it is long, cannot be regarded as cancelled where the flight is operated in accordance with the air carrier’s original planning.
Articles 5, 6 and 7 of Regulation No 261/2004 must be interpreted as meaning that passengers whose flights are delayed may be treated, for the purposes of the application of the right to compensation, as passengers whose flights are cancelled and they may thus rely on the right to compensation laid down in Article 7 of the regulation where they suffer, on account of a flight delay, a loss of time equal to or in excess of three hours, that is, where they reach their final destination three hours or more after the arrival time originally scheduled by the air carrier. Such a delay does not, however, entitle passengers to compensation if the air carrier can prove that the long delay was caused by extraordinary circumstances which could not have been avoided even if all reasonable measures had been taken, namely circumstances beyond the actual control of the air carrier.
Article 5(3) of Regulation No 261/2004 must be interpreted as meaning that a technical problem in an aircraft which leads to the cancellation or delay of a flight is not covered by the concept of ‘extraordinary circumstances’ within the meaning of that provision, unless that problem stems from events which, by their nature or origin, are not inherent in the normal exercise of the activity of the air carrier concerned and are beyond its actual control.
I am not sure you should trust my interpretation of it all and there have been a handful of other decisions on this but the text seems to suggest that you cannot avail yourself of article 5 but only of article 7 (“for the purposes of the application of the right to compensation”). The plaintiffs in the original case all completed their journey with the airline (i.e. were re-routed rather than reimbursed). In any case, because this isn't explicitly provided for in the regulation, it would seem that you would be on somewhat shaky grounds to demand compensation.