Not all watts are created equal, and all certainly don’t sound the same. Most AVRs are sort of a jack of all trades, packed with conveniences, functions, and inputs, with high watt ratings, but not necessarily focused on best audio.
Not all separates are a best effort from the manufacturer, but many are, and typically have the lion’s share of advantages over an AVR. Each separate unit has it’s own power supply, which can be fairly significant, and many tend to use superior parts and design, and often have a more refined sound as a result. The physical separation into it’s own chassis can also help improve sound. Separates also offer more flexibility with matching to another separate amp or preamp...it adds another set of interconnect cables and cost to the equation, but can actually help find tune your preferred sound.
Regardless of the wattage rating, all the separate amps I’ve owned were simply capable of doing a better job of driving the reactive load that a loudspeaker poses, and some speakers pose a tougher load than others. Many cheaper amps in AVRs and receivers are rated by driving a test resistor, not a speaker, and aren’t at their best when pushed hard or challenged by a tough load. (My separate amps have been - Hafler DH500, New York Audio Labs Moscode 300, Discrete Technology LS-2, Mitsubishi DA-A30, Stromberg Carlson ASR-120, Dynaco 70, and now twin modified Dynaco 70s with VTA boards biamped, driven with a Lazarus tube preamp).
An audio buddy of mine recently switched from a big Onkyo Integra receiver to a Linn LK85 with a Schitt Saga 2 preamp, and was astounded at how much better the Linn amp and Schitt preamp sounded. He’s now a convert. Sometimes it’s just synergy between components, but in general I think you’ll find separates to be a step up. If you get a separate amp, you may find that adding a separate preamp down the road sounds better too.