wrong shoes or weedy legs?

I started running in August and after a gentle programme of run/walk I'm now up to 20 minutes a day (yippee!), five times a week. I take things really slowly, but once I was running for 15 mins the muscle above my knee on my right leg felt awful. I wasn't sure if this was 'normal' wear and tear of 44 year old legs unaccustomed to exercise, or if it was my shoes (Mizuno Wave Riders, as recommended by a running shop after seeing me jog up and down the street). Over the past week I've been running in a pair of Reebok shoes (not sure of the model, but they're more cushioned than the Wave Riders) and my right leg has been much better. I may be asking the obvious, but do you guys think it's a shoe problem or just my legs getting used to a new way of life??