Yes, though the gap varies by item - though I have noticed Dior prices creeping up slowly over the last few seasons.Is Chanel RTW a lot more expensive than Dior RTW? I know their tweed jackets are very pricey but I'm not sure about other pieces.
One example of a huge gap: Dior tulle skirt on average is about $4k. The last Chanel tulle skirt I tried on was around $9k, and that was a couple of years ago.
Jackets: Dior classic bar jacket is about $4k, Chanel tweed jacket starts anywhere from $5.5k these days, up to $12-15k for the heavily embellished ones