Yes, brands definitely drive differently. Before we bought ours (Tesla M3 second hand) we hired a few, but our priority was range so tended to be the prestige hires which do run to larger cars so I don't know what the choice in small cars is like.
The Merc EQE (I think) was heavy, smooth and plush, kind of like a BA first class cabin (quiet and calm, but too much blue LED lighting 😂) . The Polestar was a really nice drive, devoid of personality but in a "not shouting, just gets on with it" way rather than a dull way. However I could not get on with a rear view screen instead of a phsyical mirror (obvs that is not an EV issue though). The M3 we have is smaller and nippier and better on corners because it's a sedan not an SUV, but it does still feel wide, not a small car.
I've also driven some small city car club EVs but hard to get a sense for their abilities other than one pedal driving and no "between the gear" spots makes 20 zones much less of a drag
Looks like Audio may be launching an all electric A3 soon though, so maybe a good one to try as a like for like comparison?
Body style is going to change the ride the same as it does with EVs, but with the lower weight making a difference as well.
"Engine size" as in cc isn't really a thing, but the electric motors in different cars certainly have difference performance specs and like an ICE these are deliberate differentiators so you pay more for performance. And like ICE you also have AWD, FWD or RWD. Finally, as well as range there is charging speed - some cars charge much faster for the same size battery, which makes a difference if you expect to drive beyond your range frequently which I do.
We got the M3 because it had best range in our budget (second hand teslas are really cheap right now cos Musk has tainted the brand) and the sedan body doesn't make DH carsick, which the EV SUVs did. But I do enjoy driving it. Not a fan of having no dashboard and not being able to use Android Auto with it, but again those aren't really EV issues so much as Tesla issues. One downside is it's so smooth it's easy for your speed to creep up so I really like the cruise control for long drives to keep me at a steady 70.
If you fancy hiring one to try, the big auto sites and youtubers are reviewing EVs all the time, though TBH chatGPT or Gemini is probably a good place to ask about good driver-focussed EVs.