The Evohome wall plate needs a constant mains feed so it is likely it would need some rewiring at the control end as most thermostats are switched feeds rather than constant. (I’m not an expert but this was my finding)
I fitted an Evohome to my house and was able to use the existing thermostat wires to pass mains to the thermostat but it will vary house to house I suspect. For me this wasn’t too hard because I had to rewire the switching units to the boiler valve and hot water valve anyway and changed the wires at the boiler end.
I think Nest has a battery to deal with the times it isn’t powered which is also the case for Evohome but my experience is it needs a permanent feed the batteries aren’t great.
Hope that helps.
I would say the guys at https://theevohomeshop.co.uk/en/ are very helpful and seem to answer questions before a purchase. The prices from that site are pretty good as well, that is where mine came from.
It is a great system once you have it all setup to your needs, just wish it wasn’t so expensive.