Best Host For Scalability & Large Traffic?

The answer -- as always -- is it depends.

What does your technology stack look like? And how open are you to changing it?
What exactly does "large traffic" mean? What kind of traffic is it? Are people requesting CPU intensive pages or are they just trying to download a bunch of static files? And how big are these spikes? Are these spikes predictable so that you can scale up manually or do you need your host to be able to detect the spikes and react?
How technically proficient are you? Are you looking to manage everything yourself or do you want to offload some or all of it?
Etc. etc. etc.

And even after knowing all of this, there's no one right answer. A lot just depends on you and your preferences. (You might as well ask, "What's the best ice cream, chocolate or vanilla?")

I've used both Rackspace and AWS and I personally like AWS. I like the way they implement autoscaling; I like the way you can roll your own AMIs; I like the fact that they have a lot of managed services like RDS and ElastiCache; I like their APIs. I like that we can use Ansible for configuration management and there are already modules that hook into all of AWS services that we need to. I like that there are a billion other people using AWS so it's pretty easy to find information on their most arcane services.

Are any of these things important to you? I have no idea. Furthermore, Rackspace has a lot of these features too -- and you can even use AWS through Rackspace now if that's your thing. Moreover, I imagine that the other hosts you mention also provide a lot of this sort of functionality.

I'd also suggest that there might be other things you can do outside of changing your host to increase performance in the face of traffic spikes. For instance, though our web application is CPU intensive, we use a full page caching system (in our case Varnish) so that when we get traffic spikes most of the requests are served from our load balancer's RAM rather than needing to be processed and served by our web servers. But this works for us so well because our traffic spikes are generally tied to just a few unauthenticated pages that we've linked to in social media posts. Your own usage patterns might not make full page caching a viable solution -- but maybe there's something else that is. Again, it depends.

The upshot is that you need to do your own research. You need to look at your own systems. You need to decide what's right for you.