There will probably be a slight difference in memory utilisation, but only in as much as the footprint differs between servlet containers. There is also a slight chance that you've encountered a memory leak with the container - but this is doubtful.
The most likely issue is that your application has a memory leak - in any case, the cause is more important than a quick fix - what would you do if the 'new' container just happens to last an extra week etc? Moving the problem rarely solves it...
You need to start analysing the applications heap memory, to locate the source of the problem. If your application is crashing with an OOME, you can add this to the JVM arguments.
-XX:-HeapDumpOnOutOfMemoryError
If the performance is just degrading until you restart the container manually, you should get into the routine of triggering periodic heap dumps. A timeline of dumps is often the most help, as you can see which object stores just grow over time.
To do this, you'll need a heap analysis tool:
JHat or IBM Heap Analyser or whatever your preference :)
Also see this question:
Recommendations for a heap analysis tool for Java?
Update:
And this may help (for obvious reasons):
How do I analyze a .hprof file?