From the little I know if they have cPanel and the system set up correctly if you have 4 CPU's a load average of 4 means that all CPU's are working at 100% capacity. If you have 24 CPU's then it would have to reach 24 before they are at capacity.

24 CPU's at 4.68 load average is using 19.5% of the their full capabilities.
4 CPU's at 0.50 load average is using 12.5% of the their full capabilities.

So based on those numbers you new host is working 6% harder. Which isn't a big difference and considering they have a lot of room before reaching 100% I think you should be fine.

This of course also assumes both machines are using the same exact type of CPU's and disk IO isn't an issue.

Sincerely,
Kevin.