I come from another angle on this issue;
Depending on the operating system or virtulization technology being used, the hosting company CAN limit the CPU and Memory in such a way that you're guaranteed that amount each time. Memory is usually one of the biggest factors in gaining some quick speed. Here's a quite anology on Memory;
Your website is a bathtub full of water, an empty bucket, and an empty bathtub. The bigger bucket you get, the faster you can move the water from one tub to the other.
The tub with water is your site, the bucket is memory, and the empty tub is your connection out to the web (and then to client). So if you have a 5 gallon bucket, you can move water (data) faster than if you had a 1 gallon bucket. But don't go crazy and think you can use a 20 gallon bucket as you're going to be limited by how much you can physically carry yourself (this would be the CPU).
So, back to the server;
Having a server with more memory is good, but don't go getting a server with 12GB of memory and an underpowered CPU - the server would kill itself trying to keep up, or just not use all the memory.
There's a balancing act that you need to find somewhere in the middle. Usually 1-2GB of memory on a VPS is about the mark you want to be at. Definitely going from 0.5GB memory to 1GB of memory you should see a speed increase.
Now, since you're dealing with a media rich site, have you considered a CDN (Content Delivery Network)? There are some inexpensive places like
www.maxcdn.com which can provide up to 1TB of bandwidth for $40 (not $40/year, $40 per 1 TB. If it takes you 12 months to use all that space, then you only pay the $40). I use CDN on my sites all the time. Faster delivery for the clients as the content is stored at remote servers closer to the clients.
If you're dealing with media rich sites, a CDN is something that you should definitely consider. It'll save the processing power of the CPU trying to dump out bandwidth etc on your existing VPS. And since you're using Wordpress too, they're also compatible with many CDN's too.
It all depends on what your current limitations are with the CPU assigned to the server right now. I'm guesing you don't have access to the entire CPU amount (or do you?). What kind of load is generated on your container? What is the bandwidth being used currently? Disk space needed? Free memory? Stability?
There's lots of factors, and it's entirely possible that just putting more memory into the existing machine is all you need. What are your reasons for wanting to upgrade/move right now? Are things slow, or you're just looking at the age of things?