Another important consideration is the field of view. From memory I think you are using a 14″ Celestron or Meade. This will have a long focal length so the field of view in your guide camera will be quite small.
Also, spectrograph guide optics are not that great, though the optics in the updated Lhires III from a few years ago are much better. I think you have one of these models? The point here is I am not sure how wide a usable field of view you get from the guide optics.
The best way to find out would be to try each of the cameras you mention. The Atik 314 will give you a larger field of view, so that can be used to find out if there is a usable wider field than you get in the Lodestar.
The frame rate should not matter. I have never used a frame rate faster than 1 image every 5 seconds for guiding, and up to 30 seconds in a field without a bright star. Anything faster and you risk your mount chasing the seeing rather than guiding. I think you have a good quality mount, so guide exposures of 10’s seconds should not be a problem. So you don’t need the high frame rate from CMOS chips. However, a fast download speed (CMOS or CCD) is an advantage as you can start the next guide exposure quickly.
My personal experience is the Lodestar is very good for guiding. It shows a few hot pixels as it is an uncooled camera, but they’ve never caused me major problems. If replacing the Lodestar with another camera, then as pointed out by Robin you need to be careful that the guide camera is small enough to fit next to your spectrum imaging camera. You might also want to consider the weight depending on the kind of focuser you are using.