If you intend to do only web browsing, checking emails, using MS office then the new macbook will be relatively faster than even your 2009 macbook pro. Note that the new macbook however equipped with a basic intel Core M processor, is equipped with a much more advanced PCI storage SSD. In comparison the SSD on your Macbook will be relatively a bit slower to respond.
So, the end result will be much faster loading of web browser, faster loading of email, faster loading of MS office and even faster loading of photoshop elements and faster boot. Also, the internet connectivity will be better, as it comes with AC connectivity.
BUT
The new macbook will be missing the RAW power of your 2009 macbook pro only if your macbook pro can be equipped with 8 GB RAM (8GB is Max). 4 GB RAM on you macbook pro can be a thing to worry as you won’t be able to multitask but you can upgrade it to Max 8 GB on a 2009 machine. The processor doesn’t matter because even the older core 2 duo will throw the intel Core M processor out of water....😁 😁
Hope this helps.....