I like the ease of deployment these 2 offer compared to mysql/sql server etc.
Which scales better in terms of performance and is less prone to corruption in a multiuser environment as the number of users grows?
I have worked with access/jet but not with sqlite.
My experience with access is that it works well enough in the situations in which I use it, small, cabled, LANs but that there can be corruption problems when the network isn't rock solid. Also it doesn't seem to work at all well on wireless networks (at least for me).
You might want to check out SqLite's 'appropriate uses' page here. It lists pros/cons of using sqlite in various scenarios. However, it should stand up pretty well against Access, provided you're not going to use it for concurrent access from multiple processes from multiple machines.
MS Access has a number of limits which you may want to check out here, e.g. max DB size of 2GB, max 255 concurrent users, etc. SqLite scales higher than these limits in almost all cases I think.
EDIT: One other thing: SqLite doesn't offer password-encrypted databases as standard, whereas MS Access obviously does. SqLite does have a proprietary extension for encryption though, by the same developers who write SqLite: