If you are OK with the smaller and lower res screen, it will be faster as far as the CPU and hard-drive goes. You may just look into getting more RAM and a newer SSD hard drive for yours, will be about $100 and I think it will run as fast at a cheap laptop. Two matching 2GB RAM sticks are about $30 and will give you dual channel speeds, another $70 for a 256 GB SSD, laptop will feell like new. If you want to spend the extra on a new system, you'll get a faster CPU but will have a slower hard drive (once you swap it for a new one) and lower quality screen. Your current laptop even if it's older, is higher quality than any new system under $500, outside of the slower CPU and RAM. If this was my system, I'd upgrade it for the $100 before buying a new one, if the issue was just slowness with several tabs open.
On the other hand, if you feel like getting something new, you should be able to sell your laptop for at least $100 and get some money towards a new system.