What computer would run minecraft faster?

So I play minecraft on very big servers and I'm wondering which computer will run it faster without as much lag.

The first an hp 15 notebook laptop

4 gb of ram and memory
500 gb sata hardrive
Accelerated processor

The second is a acer aspire axc desktop
4gb of ram and memory
500 gb sata hardrive
Intel had graphics
Intel Celeron processor

They both cost exactly the same at 258.

Both would do well

Okay so the first laptop; HP is a well known brand but is common for overheating so make sure to keep your vents clear.
By accelerated processor I think you mean AMD's new APU. This means it has advanced graphics on board as well as the CPU. This means better graphical performance withoutthe masive price tag. I have an A10 in my personal laptop and it runs (in your interest) Minecraft on high at around 50fps on hypixel.net
APU's will use your RAM for graphics memory so the possibility to upgrading to 6-8GB in the future should be ideal if you want the best performance for your money.
Forget about the second laptop. That Intel Celeron will be of no ue to you at all for gaming, it is actually one of the worst CPU's Intel has ever made… Ever. It may advertise Intel HD Graphics but they are S***!
Trust me man. Choose laptop number one and keep your laptop cool.

Game on, man!

Without looking at specific models I can give a definite answer but Accelerated processors are better a running games usually

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The second computer sounds like it would be better since it has a graphics card, which helps the computer handle graphics, especially with games.

The second machine will absolutely not be adequate. Its graphics are inferior and the Celeron processors are completely inappropriate for gaming other than with browser based games.

Unfortunately, you didn't tell us which processor and some other details about the first one. I suggest you search google for "minecraft recommended hardware" and select the link for "game-debate.com". On the page that comes up, scroll down a ways and you will find a place where you can enter your CPU and GPU models and it will tell you how well it will perform with that hardware.