I've read several posts about the Bus Pirate being used as a logic analyzer. Therefore I wonder how the Logic Pirate and Bus Pirate compare to each other when it comes to analyzing logic signals.

As far as I can tell the main difference is in the sample rate. The Logic Pirate has a sample rate of 20MHz, where the Bus Pirate's sample rate is <1MHz. Correct? I can imagine that the Bus Pirate might be fast enough in some cases and having the additional possibilities at hand might be an advantage.

Can anyone tell me if there are more things to consider when choosing between the two?

It seems to me that a lot more people use the Bus Pirate than the Logic Pirate, and from that follows that if you actually want to have a good time working WITH the tools and not ON the tools, then you (OP, or reader from the future) should get the Bus Pirate. For example while Bus Pirate is supported by sigrok, the Logic Pirate is not. Neither one of the devices seem to have gotten any updates in the last two years, so any problem you encounter you will probably have to solve yourself.

I have both the devices, and never actually used the Logic Pirate, and the Bus Pirate I only used for sniffing known signals.