Much of the core technology isn't that different, significantly because they first restricted and then effectively froze development a few years ago, but the engines aren't 3l V10s any more but 2.4l V8s.
In the time of the 3l V10s, from memory they peaked at over 900bhp. For a while they were revving to about 19,000, but as the materials science for this got increasingly complex they restricted it to about 17,000 on cost grounds - after all there's no real sporting value to everyone spending an extra $50m to get to exactly the same relative performances with little noticeable difference in outcomes.
The 2.4l V8s were about 750ish from memory when they came in; I've not heard more recent figures but due to development restrictions I doubt they're much different. The other interesting technology now is the extra hybrid power source and the large kick that can offer; interestingly it was very nearly raced (in a different form) by McLaren in 1998, though a late rule change that was suspected to be at the behest of another team banned it.
Otherwise - the core reason the engines are recognisable is that they're required in the rules to be so. Turbos were restricted then banned in 1998 after, at the design peak in 1986, reaching 1500bhp from 1.5l engines. They're quite likely to be back in a few years though, albeit in a very different form to their mid-80s incarnation. Turbines - what I suspect we'd actually be running otherwise, although indirectly as electric generators for capacitor packs - were banned even earlier. I don't think Wankel engines have ever been legal in F1. Diesel definitely isn't.
When we say recognisable though, I'm not sure people realise just how alien these engines are within the limits of a piston engine. They barely do anything below what would be red-line revs for a road car and generate almost no power until they're past 12-13,000RPM. Piston speeds are firmly supersonic and the elasticity of the metal needs to be factored in, yet I read once that the pistons were getting so close to the tops of the cylinder heads in combustion that there was a visible ring of clear metal in the combustion deposits because there wasn't space there for the deposits to form. The real shock though is the noise; we're all used to what a road performance engine sounds like, but a 17,000RPM V8 (and even more so a 19,000RPM V10) howls and screams like no road engine you'll ever hear, bike included. Animalistic, harsh, edgy and the sort of sound that lives with you; TV doesn't come close to capturing it.