Short answer is yes a 50cc is going to cut that size wood faster. Even my modified narrow kerf chained 30cc class climbing saws will not keep up with a high quality pro grade 50cc.
Honestly, I don’t think I would ever put a 12 or 14” bar on a 50cc saw. I use 16,18, and 20 inch on my 50cc saws depending on the application. That’s just my preference though.
Not all, but some other factors that play into it are chain speed and type. Some saws have faster chain speeds therefore are usually going to cut faster when used properly. It is very difficult to explain every aspect that influences how fast a saw cuts.
More importantly, if you can handle a 50cc saw without issues then go for it as it will cut faster and be less bending or over reaching.