I think the standard height for base cabinets in general is 36"/ I don't know why yours would be shorter than that. Or was the old one taller? I think it really comes down to your personal preference. Sometimes tall people will bump up the heights of their cabinets especially in the kitchen to bring work surfaces to a more confortable level.
Kitchen cabinets are nominally 34" high and 24" deep. 34' will yield a finished height of 36", assuming a 2" countertop.
On the other hand you will see a lot of variance from for vanity/bathroom cabinets. Traditionally, vanities were shorter (31" - 32") and not as deep (21"). Modern vanities size varies from one product line to the next.
Should you raise the cabinet? It will depend on the answer to a few questions:
1) What type of sink are you using? The cabinet is usually higher with an undermount and lower with vessel sink.
2) Will children use the bathroom and ages? With childrem you may need a lower sink
3) Height of the people using the sink?
4) What feels confortable to you? My wife and I like to to fill both hands with water then splash on our faces. So we discovered we like our sink higher than normal.
In my typical micro analysis method, my wife and I like a 35 inch cabinet with counter top when used with 4 to 5 inch deep vessel sink. We took the old vanity and raised and lowered it until we found the comfort range.
If you raise the cabinet split the shimming between the top and bottom. 1/4 round molding can cover the bottom and depending on the counter top you can place 1/2 to 3/4 plywood under it and won't show. If you raise just the bottom more than 1/2, the cabinets will look out of proportion.