Shimano Alivio M4000 vs Altus M370 shifters
When you upgrade shifters (provided you have the right compatibility), you're paying for (or trading off between):


Lower weight
More strength/durability 
Reliability 


In the sense that Alivio > Altus, you should be getting some of these. 

However, if your shifters and what not are in good condition (i.e. good cable runs, shifters in good condition, derailleur in good condition), I don't think you'll notice (much).