First thing is to compare both skates on the same ice surface like hockeydad3 said. outdoor ice is very different.
Other than the steel height difference that was mentioned, Also get your old skate profile measured. who knows what is on there??? That's an important piece of info. After many sharpenings, your old blades could have gone very banana'd, and/or flat in the middle with banana'd ends. If you find a flat center section, maybe you prefer a center glide profile? Quads are heal glide. Example of an old popular center glide profile is the old MAX Edge 981, or a CAG Profile that have a flat glide area in the middle of the blade. I still profile some players with that 981, although the Quads (OMNI Quads that I use) are becoming much more popular. But it is all personal Preference. The 981 has lots of blade contact but you need to be an elite skater to know how to use the various area's of the blade to turn or use the all out speed it can offer in the middle of the blade. Hence why the Quads / OMNI QUADS and elipse profiles are easier to skate on.
Lastly, measure the steel height at the front and back of each pair of skates to get an idea of the pitch you have on each pair. essentially you are measuring how much less steel you have on the front vs the rear. you might be pitch forward more on the Quad 0.5 that you are on your old pair, and that's the root cause of what you are feeling.
I'm giving you a lot of info here, sometimes brining in both skates to a pro and asking these questions can help. When I profile skates for someone, I always ask to see the old blades so I can measure them. Even if I'm doing mail order Profiling, I ask for a high res image of the old steel for analysis.
Young ones adapt so quickly to new Profiles. Sometimes the smallest change really messes up us old guys 😉