How to know if a Arduino has enough memory for a project

The faster execution has not been evident in practice, and I doubt the OP will see it either. Convenience is hardly the word for it. The difference between being able to do the job and not being able to do the job is not a matter of convenience, it's a matter of having the right tool.

And, despite liudr's self-aggrandisement, I submit that the Uno is the wrong tool for the job or, even if it is OK now, it will be wrong soon enough.

So, in the light of the OP having no more gold stars than I do, and the minor extra cost, he/she would be wiser not to bother with a Uno.