I'm wondering if I was to run minecraft in a 32bit or 64bit ubuntu server; would there be a benefit (speed improvements) or something else, or just the same? Downsides?
Minecraft is written in Java, so it should "adapt" itself to both 32-bit and 64-bit systems (depending if you have a 32-bit or 64-bit Java runtime).
While Minecraft itself is not optimized for 64-bit, it will take advantage of JVM optimizations for 64-bit processors. Basically, this means more general-purpose registers available (16 in 64-bit against 8 in 32-bit, which means better machine code and less RAM access, improving performance) and larger addressable memory. On the other hand, since now pointers take up twice as much space, there is a little extra overhead for using 64-bit.
But you should also think about the operating system, as it will also take advantage of 64-bit improvements. If you have more than 2GB or 3GB of RAM, your operating system should be 64-bit, else it won't access all RAM (or will have a considerable overhead doing so). And if you have a 64-bit operating system, you should also go with a 64-bit Java Runtime for better performance (as other users already commented).
By the way, in my opinion, you should always go to 64-bit unless you have a very good reason to avoid it, like compatibility reasons (which is not this case).
Related question on StackOverflow: Does Java 64bit perform better than the 32bit version?
Wait a minute! I talked code written in Java, but how about native libraries? Like OpenGL support and OpenAL? They are available on both 32-bit and 64-bit versions, and the correct version will be loaded. And I can confirm that on my Linux 64-bit system, it loads the 64-bit version of those native Java libraries. (as an experiment, I've deleted the 32-bit versions and Minecraft still runs fine)
Minecraft is not designed as a 64-bit application, and thus, while usable on a 64-bit OS, won't see any sorts of improvements from a technical standpoint.
However, if you also install the 64-bit java runtime environment, you may notice some slight performance optimization, but a 64-bit OS on its own will not have much of an effect.
I'm running my server on a 64 CentOs server and it doesn't seem to have improved anything. Minecraft only records the movements X,Y,Z of the players with items and block placed in the world. So running it on a 32 or 64 bit OS won't change anything.
For better performance of the game you need lots of RAM and fast HDD maybe a 10k RPM or 15 RPM on the server. That way you ensure faster loading and higher efficiency.
I have 8GB RAM on a Quad core system with 2 HDD 10k RPM, and I haven't noticed any lag with 20+ players online.