Yes, the car will make a good start on the hill (which might be, say, three blocks long, maybe a 5 - 7% grade) running strongly for perhaps 10 seconds and then there will be a sudden loss of power. It happens in third or fourth, at various speeds (once on a freeway bridge at 60 mph).
I've just come back from a run in the car around the neighbourhood, on level streets mainly, but with one quite steep uphill, which the car took with no problem in mostly second gear, changing to third towards the top. There's good response from the accelerator if I floor it suddenly, the response, of course, varying depending on the gear. So generally just driving around the engine feels quite strong; just the long higher-speed hills seem to be the issue.
I have another question, possibly related, that I think I will put in another thread, as I don't want this one to get off the topic: sudden loss of power on hills in higher gears.