It will run just as well, better if you consider that you won't have to select the OS every time you start your machine.
The only thing you may want to consider is if there are certain Windows specific apps that you use. Then you may want to try installing those apps on your Ubuntu and see how well they run in Wine, Cross-Over Linux or Plan-on-Linux.
I have had Ubuntu installed on my laptop solely for about 5 years, and have never had any performance issues (my laptop originally came with Vista Home Premium, so Ubuntu was a spectacular upgrade and I've never looked back!)
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